geom charts - exercise 4

8/12/2019 Geom Charts - Exercise 4

1/51

x y

-2 3

5 3

-1 11

-8 -8

x y

-2 3

5 3

-1 11

-8 -8-2 3

-11

-10

-9-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

8

9

10

11

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 1

-11

-10

-9

-8

-7-6

-5

-4

-3

-2

-1

0

1

2

3

4

56

7

8

9

10

11

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7


2/51

x y

0 -1

1 0

3 2

x y

-3 0

-1 -2

5 4

-3 0

x y

1 19 -7

0 -8

1 1

0 11-5

-4

-3

-2-1

0

1

2

3

4

5

-5 -4 -3 -2 -1 0 1 2 3 4 5

-5

-4

-3

-2

-1

0

1

2

3

4

5

-5 -4 -3 -2 -1 0 1 2 3 4 5

8 9 10 11

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

8

910

11

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0


3/51

1 2 3 4 5 6 7 8 9 10 11


4/51

121

11.04536 30.5


5/51

x y

-1 1

3 -4

2 4

-1 1

x y

8 7

0 -6

-3 -5

8 7

-5

-4

-3

-2-1

0

1

2

3

4

5

-5 -4 -3 -2 -1 0 1 2 3 4 5

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

67

8

9

10

11

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7


6/51

x y

-1 6

2 -4

-4 0

-1 6

8 9 10 11

-7

-6

-5

-4

-3

-2

-1

01

2

3

4

5

6

7

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7


7/51


8/51

x y

0 -7

6 1

12 9

-3 -11

-12 -23

1.333333

4

3

0.867008

0.620249 0.197432

0.714286 0.714286

-9-8-7-6-5-4-3-2-101

23456789

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9


9/51

x y

0 2.33

2 -7.66667

4 -17.6667

-1 7.333333

-2 12.33333

-5

-5

1

TRUE

-9.00-8.00-7.00-6.00-5.00-4.00-3.00-2.00-1.000.001.00

2.003.004.005.006.007.008.009.00

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9


10/51

x y

0 0

14 10

28 20

-7 -5

-56 -40

0.714286

5

7

-9-8-7-6-5-4-3-2-101

23456789

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9


11/51

x y

0 0

10 -16

20 -32

-5 8

-30 48

-1.6

-8

5

-9-8-7-6-5-4-3-2-101

23456789

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9


12/51

x y

0 -4.375

16 1.625

32 7.625

-8 -7.375

-72 -31.375

0 0.12516 6.125

32 12.125

-8 -2.875

-72 -26.875

0.375

3

8

-9-8-7-6-5-4-3-2-101

23456789

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

-9-8-7-6-5-4-3

-2-10123456789

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9


13/51

-72 -26.875

-8 -2.875

32 12.12516 6.125

0 0.125

0


14/51

h k r (x - h)2 + (y - k)2 = r2 Radius r=((x_0-x_1)^2 + (y_0-y_1)^2)

-4 -5 5.082 (x - )^2 r=((h-x_1)^2 + (k-y_1)^2)

(y - r=((-4--5.39622641509434)^2 + (-5--0.

-1 r=((-4--5.39622641509434)^2 + (-5--0.

r=((1.39622641509434)^2 + (-4.88679

1 0 1.082 -5 r=((1.39622641509434)^2 + (-4.88679

2 0.017453 1.081226 -4.91131 r=(1.94944820220719 + 23.880740473 0.034907 1.078904 -4.82264 r=(25.8301886 (25.8301886792453)

4 0.05236 1.075035 -4.73403 r = 5.08234086610149

5 0.069813 1.069621 -4.6455 (x -(-4))^2 + (y - (-5))^2 = r^2

6 0.087266 1.062661 -4.55707 (x -(-4))^2 + (y - (-5))^2 = ((25.8301886

7 0.10472 1.05416 -4.46879

8 0.122173 1.04412 -4.38066 Circle (x -(-4))^2 + (y - (-5))^2 = 5.082^2

9 0.139626 1.032542 -4.29272 (x + 4)^2 + (y + 5)^2 = 25.827

10 0.15708 1.019432 -4.205 x^2 -8x + 16 + y^2 -10y + 25 = 25.827

11 0.174533 1.004793 -4.11752 x^2 + y^2 -8x -10y + 16 + 25 = 25.827

12 0.191986 0.988629 -4.03031 x^2 + y^2 -8x -10y + 41 = 25.827

13 0.20944 0.970946 -3.94339 x^2 + y^2 -8x -10y = 25.827-41

14 0.226893 0.951749 -3.8568 x^2 + y^2 -8x -10y = -15.173

15 0.244346 0.931043 -3.77055 X_1 y_1

16 0.261799 0.908835 -3.68468 -5.39623 -0.113207547

17 0.279253 0.885132 -3.59921

18 0.296706 0.859941 -3.51417 5.082341

19 0.314159 0.833269 -3.42958 2 -7 10

20 0.331613 0.805125 -3.34546 2x-7y + 10 = 0

21 0.349066 0.775518 -3.26185 -7y = -2x-10

22 0.366519 0.744456 -3.17877 y = -2/-7 x-10/-7 -2/-7 x-10/ -0.28571

23 0.383972 0.711948 -3.09625 -7/-7 y = 2/7 x+10/724 0.401426 0.678006 -3.0143 y = 2/7 x+10/7

25 0.418879 0.642638 -2.93296 slope of tangent line

26 0.436332 0.605856 -2.85225 m_t = -2/-7 2/-7

27 0.453786 0.567671 -2.7722 tangent line is perpendicular to radius line thus rad

28 0.471239 0.528095 -2.69282 m_r = -7/2

29 0.488692 0.48714 -2.61415 substituting the center to get the equation of the r

30 0.506145 0.444817 -2.5362 y=mx+b y=mx+b

31 0.523599 0.401141 -2.459 y=-7/2 x+b y=4/3 x+b

32 0.541052 0.356124 -2.38258 -5=(-7/2)(-4)+b -7/2 x +-28 7=(4/3)(-1)

33 0.558505 0.30978 -2.30695 -5=28/2 +b 7 7=-4/3+b

34 0.575959 0.262124 -2.23214 -5-28/2=b 7+4/3=b

35 0.593412 0.213169 -2.15818 b = -38/2 b=25/3

36 0.610865 0.162931 -2.08508 y=-7/2 x+-38/2

37 0.628319 0.111424 -2.01288 solving for the system of equations to get the tang

38 0.645772 0.058666 -1.94158 -7/2 x+-38/2 = -2/-7 x-10/-7

39 0.663225 0.004671 -1.87121 -49 x+-266 = 4 x20

40 0.680678 -0.05054 -1.80179 -49 x -4 x = 20+266

41 0.698132 -0.10696 -1.73335 -53 x = 286 -5.39623


15/51

42 0.715585 -0.16457 -1.66591 x = -286 / 53 x -286 / 53

43 0.733038 -0.22334 -1.59948 y = 2/7 x+10/7 y -42/371

44 0.750492 -0.28326 -1.53408 y = (2/7) (-286 / 53)+10/7 y=-572/371

45 0.767945 -0.34432 -1.46975 y = -10.7924528301887/7+10/7 y=-572/371

46 0.785398 -0.40648 -1.40648 y = -0.79245283018868/7 y=-42/371

47 0.802851 -0.46975 -1.34432 y = -0.113207547169811

48 0.820305 -0.53408 -1.28326 tangent point is at (-286 / 53 , -42/371)49 0.837758 -0.59948 -1.22334

50 0.855211 -0.66591 -1.16457

51 0.872665 -0.73335 -1.10696

52 0.890118 -0.80179 -1.05054

53 0.907571 -0.87121 -0.99533

54 0.925025 -0.94158 -0.94133

55 0.942478 -1.01288 -0.88858

56 0.959931 -1.08508 -0.83707

57 0.977384 -1.15818 -0.78683

58 0.994838 -1.23214 -0.73788

59 1.012291 -1.30695 -0.69022

60 1.029744 -1.38258 -0.64388

61 1.047198 -1.459 -0.59886

62 1.064651 -1.5362 -0.55518

63 1.082104 -1.61415 -0.51286

64 1.099557 -1.69282 -0.4719

65 1.117011 -1.7722 -0.43233

66 1.134464 -1.85225 -0.39414

67 1.151917 -1.93296 -0.35736

68 1.169371 -2.0143 -0.32199

69 1.186824 -2.09625 -0.2880570 1.204277 -2.17877 -0.25554

71 1.22173 -2.26185 -0.22448

72 1.239184 -2.34546 -0.19487

73 1.256637 -2.42958 -0.16673

74 1.27409 -2.51417 -0.14006

75 1.291544 -2.59921 -0.11487

76 1.308997 -2.68468 -0.09116

77 1.32645 -2.77055 -0.06896

78 1.343904 -2.8568 -0.04825

79 1.361357 -2.94339 -0.02905

80 1.37881 -3.03031 -0.01137

81 1.396263 -3.11752 0.004793

82 1.413717 -3.205 0.019432

83 1.43117 -3.29272 0.032542

84 1.448623 -3.38066 0.04412

85 1.466077 -3.46879 0.05416

86 1.48353 -3.55707 0.062661

87 1.500983 -3.6455 0.069621

88 1.518436 -3.73403 0.075035


16/51

89 1.53589 -3.82264 0.078904

90 1.553343 -3.91131 0.081226

91 1.570796 -4 0.082

92 1.58825 -4.08869 0.081226

93 1.605703 -4.17736 0.078904

94 1.623156 -4.26597 0.075035

95 1.640609 -4.3545 0.06962196 1.658063 -4.44293 0.062661

97 1.675516 -4.53121 0.05416

98 1.692969 -4.61934 0.04412

99 1.710423 -4.70728 0.032542

100 1.727876 -4.795 0.019432

101 1.745329 -4.88248 0.004793

102 1.762783 -4.96969 -0.01137

103 1.780236 -5.05661 -0.02905

104 1.797689 -5.1432 -0.04825

105 1.815142 -5.22945 -0.06896

106 1.832596 -5.31532 -0.09116

107 1.850049 -5.40079 -0.11487

108 1.867502 -5.48583 -0.14006

109 1.884956 -5.57042 -0.16673

110 1.902409 -5.65454 -0.19487

111 1.919862 -5.73815 -0.22448

112 1.937315 -5.82123 -0.25554

113 1.954769 -5.90375 -0.28805

114 1.972222 -5.9857 -0.32199

115 1.989675 -6.06704 -0.35736

116 2.007129 -6.14775 -0.39414117 2.024582 -6.2278 -0.43233

118 2.042035 -6.30718 -0.4719

119 2.059489 -6.38585 -0.51286

120 2.076942 -6.4638 -0.55518

121 2.094395 -6.541 -0.59886

122 2.111848 -6.61742 -0.64388

123 2.129302 -6.69305 -0.69022

124 2.146755 -6.76786 -0.73788

125 2.164208 -6.84182 -0.78683

126 2.181662 -6.91492 -0.83707

127 2.199115 -6.98712 -0.88858

128 2.216568 -7.05842 -0.94133

129 2.234021 -7.12879 -0.99533

130 2.251475 -7.19821 -1.05054

131 2.268928 -7.26665 -1.10696

132 2.286381 -7.33409 -1.16457

133 2.303835 -7.40052 -1.22334

134 2.321288 -7.46592 -1.28326

135 2.338741 -7.53025 -1.34432


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136 2.356194 -7.59352 -1.40648

137 2.373648 -7.65568 -1.46975

138 2.391101 -7.71674 -1.53408

139 2.408554 -7.77666 -1.59948

140 2.426008 -7.83543 -1.66591

141 2.443461 -7.89304 -1.73335

142 2.460914 -7.94946 -1.80179143 2.478368 -8.00467 -1.87121

144 2.495821 -8.05867 -1.94158

145 2.513274 -8.11142 -2.01288

146 2.530727 -8.16293 -2.08508

147 2.548181 -8.21317 -2.15818

148 2.565634 -8.26212 -2.23214

149 2.583087 -8.30978 -2.30695

150 2.600541 -8.35612 -2.38258

151 2.617994 -8.40114 -2.459

152 2.635447 -8.44482 -2.5362

153 2.6529 -8.48714 -2.61415

154 2.670354 -8.5281 -2.69282

155 2.687807 -8.56767 -2.7722

156 2.70526 -8.60586 -2.85225

157 2.722714 -8.64264 -2.93296

158 2.740167 -8.67801 -3.0143

159 2.75762 -8.71195 -3.09625

160 2.775074 -8.74446 -3.17877

161 2.792527 -8.77552 -3.26185

162 2.80998 -8.80513 -3.34546

163 2.827433 -8.83327 -3.42958164 2.844887 -8.85994 -3.51417

165 2.86234 -8.88513 -3.59921

166 2.879793 -8.90884 -3.68468

167 2.897247 -8.93104 -3.77055

168 2.9147 -8.95175 -3.8568

169 2.932153 -8.97095 -3.94339

170 2.949606 -8.98863 -4.03031

171 2.96706 -9.00479 -4.11752

172 2.984513 -9.01943 -4.205

173 3.001966 -9.03254 -4.29272

174 3.01942 -9.04412 -4.38066

175 3.036873 -9.05416 -4.46879

176 3.054326 -9.06266 -4.55707

177 3.071779 -9.06962 -4.6455

178 3.089233 -9.07504 -4.73403

179 3.106686 -9.0789 -4.82264

180 3.124139 -9.08123 -4.91131

181 3.141593 -9.082 -5

182 3.159046 -9.08123 -5.08869


18/51

183 3.176499 -9.0789 -5.17736

184 3.193953 -9.07504 -5.26597

185 3.211406 -9.06962 -5.3545

186 3.228859 -9.06266 -5.44293

187 3.246312 -9.05416 -5.53121

188 3.263766 -9.04412 -5.61934

189 3.281219 -9.03254 -5.70728190 3.298672 -9.01943 -5.795

191 3.316126 -9.00479 -5.88248

192 3.333579 -8.98863 -5.96969

193 3.351032 -8.97095 -6.05661

194 3.368485 -8.95175 -6.1432

195 3.385939 -8.93104 -6.22945

196 3.403392 -8.90884 -6.31532

197 3.420845 -8.88513 -6.40079

198 3.438299 -8.85994 -6.48583

199 3.455752 -8.83327 -6.57042

200 3.473205 -8.80513 -6.65454

201 3.490659 -8.77552 -6.73815

202 3.508112 -8.74446 -6.82123

203 3.525565 -8.71195 -6.90375

204 3.543018 -8.67801 -6.9857

205 3.560472 -8.64264 -7.06704

206 3.577925 -8.60586 -7.14775

207 3.595378 -8.56767 -7.2278

208 3.612832 -8.5281 -7.30718

209 3.630285 -8.48714 -7.38585

210 3.647738 -8.44482 -7.4638211 3.665191 -8.40114 -7.541

212 3.682645 -8.35612 -7.61742

213 3.700098 -8.30978 -7.69305

214 3.717551 -8.26212 -7.76786

215 3.735005 -8.21317 -7.84182

216 3.752458 -8.16293 -7.91492

217 3.769911 -8.11142 -7.98712

218 3.787364 -8.05867 -8.05842

219 3.804818 -8.00467 -8.12879

220 3.822271 -7.94946 -8.19821

221 3.839724 -7.89304 -8.26665

222 3.857178 -7.83543 -8.33409

223 3.874631 -7.77666 -8.40052

224 3.892084 -7.71674 -8.46592

225 3.909538 -7.65568 -8.53025

226 3.926991 -7.59352 -8.59352

227 3.944444 -7.53025 -8.65568

228 3.961897 -7.46592 -8.71674

229 3.979351 -7.40052 -8.77666


19/51

230 3.996804 -7.33409 -8.83543

231 4.014257 -7.26665 -8.89304

232 4.031711 -7.19821 -8.94946

233 4.049164 -7.12879 -9.00467

234 4.066617 -7.05842 -9.05867

235 4.08407 -6.98712 -9.11142

236 4.101524 -6.91492 -9.16293237 4.118977 -6.84182 -9.21317

238 4.13643 -6.76786 -9.26212

239 4.153884 -6.69305 -9.30978

240 4.171337 -6.61742 -9.35612

241 4.18879 -6.541 -9.40114

242 4.206243 -6.4638 -9.44482

243 4.223697 -6.38585 -9.48714

244 4.24115 -6.30718 -9.5281

245 4.258603 -6.2278 -9.56767

246 4.276057 -6.14775 -9.60586

247 4.29351 -6.06704 -9.64264

248 4.310963 -5.9857 -9.67801

249 4.328417 -5.90375 -9.71195

250 4.34587 -5.82123 -9.74446

251 4.363323 -5.73815 -9.77552

252 4.380776 -5.65454 -9.80513

253 4.39823 -5.57042 -9.83327

254 4.415683 -5.48583 -9.85994

255 4.433136 -5.40079 -9.88513

256 4.45059 -5.31532 -9.90884

257 4.468043 -5.22945 -9.93104258 4.485496 -5.1432 -9.95175

259 4.502949 -5.05661 -9.97095

260 4.520403 -4.96969 -9.98863

261 4.537856 -4.88248 -10.0048

262 4.555309 -4.795 -10.0194

263 4.572763 -4.70728 -10.0325

264 4.590216 -4.61934 -10.0441

265 4.607669 -4.53121 -10.0542

266 4.625123 -4.44293 -10.0627

267 4.642576 -4.3545 -10.0696

268 4.660029 -4.26597 -10.075

269 4.677482 -4.17736 -10.0789

270 4.694936 -4.08869 -10.0812

271 4.712389 -4 -10.082

272 4.729842 -3.91131 -10.0812

273 4.747296 -3.82264 -10.0789

274 4.764749 -3.73403 -10.075

275 4.782202 -3.6455 -10.0696

276 4.799655 -3.55707 -10.0627


20/51

277 4.817109 -3.46879 -10.0542

278 4.834562 -3.38066 -10.0441

279 4.852015 -3.29272 -10.0325

280 4.869469 -3.205 -10.0194

281 4.886922 -3.11752 -10.0048

282 4.904375 -3.03031 -9.98863

283 4.921828 -2.94339 -9.97095284 4.939282 -2.8568 -9.95175

285 4.956735 -2.77055 -9.93104

286 4.974188 -2.68468 -9.90884

287 4.991642 -2.59921 -9.88513

288 5.009095 -2.51417 -9.85994

289 5.026548 -2.42958 -9.83327

290 5.044002 -2.34546 -9.80513

291 5.061455 -2.26185 -9.77552

292 5.078908 -2.17877 -9.74446

293 5.096361 -2.09625 -9.71195

294 5.113815 -2.0143 -9.67801

295 5.131268 -1.93296 -9.64264

296 5.148721 -1.85225 -9.60586

297 5.166175 -1.7722 -9.56767

298 5.183628 -1.69282 -9.5281

299 5.201081 -1.61415 -9.48714

300 5.218534 -1.5362 -9.44482

301 5.235988 -1.459 -9.40114

302 5.253441 -1.38258 -9.35612

303 5.270894 -1.30695 -9.30978

304 5.288348 -1.23214 -9.26212305 5.305801 -1.15818 -9.21317

306 5.323254 -1.08508 -9.16293

307 5.340708 -1.01288 -9.11142

308 5.358161 -0.94158 -9.05867

309 5.375614 -0.87121 -9.00467

310 5.393067 -0.80179 -8.94946

311 5.410521 -0.73335 -8.89304

312 5.427974 -0.66591 -8.83543

313 5.445427 -0.59948 -8.77666

314 5.462881 -0.53408 -8.71674

315 5.480334 -0.46975 -8.65568

316 5.497787 -0.40648 -8.59352

317 5.51524 -0.34432 -8.53025

318 5.532694 -0.28326 -8.46592

319 5.550147 -0.22334 -8.40052

320 5.5676 -0.16457 -8.33409

321 5.585054 -0.10696 -8.26665

322 5.602507 -0.05054 -8.19821

323 5.61996 0.004671 -8.12879


21/51

324 5.637413 0.058666 -8.05842

325 5.654867 0.111424 -7.98712

326 5.67232 0.162931 -7.91492

327 5.689773 0.213169 -7.84182

328 5.707227 0.262124 -7.76786

329 5.72468 0.30978 -7.69305

330 5.742133 0.356124 -7.61742331 5.759587 0.401141 -7.541

332 5.77704 0.444817 -7.4638

333 5.794493 0.48714 -7.38585

334 5.811946 0.528095 -7.30718

335 5.8294 0.567671 -7.2278

336 5.846853 0.605856 -7.14775

337 5.864306 0.642638 -7.06704

338 5.88176 0.678006 -6.9857

339 5.899213 0.711948 -6.90375

340 5.916666 0.744456 -6.82123

341 5.934119 0.775518 -6.73815

342 5.951573 0.805125 -6.65454

343 5.969026 0.833269 -6.57042

344 5.986479 0.859941 -6.48583

345 6.003933 0.885132 -6.40079

346 6.021386 0.908835 -6.31532

347 6.038839 0.931043 -6.22945

348 6.056293 0.951749 -6.1432

349 6.073746 0.970946 -6.05661

350 6.091199 0.988629 -5.96969

351 6.108652 1.004793 -5.88248352 6.126106 1.019432 -5.795

353 6.143559 1.032542 -5.70728

354 6.161012 1.04412 -5.61934

355 6.178466 1.05416 -5.53121

356 6.195919 1.062661 -5.44293

357 6.213372 1.069621 -5.3545

358 6.230825 1.075035 -5.26597

359 6.248279 1.078904 -5.17736

360 6.265732 1.081226 -5.08869

361 6.283185 1.082 -5


22/51

113207547169811)^2)

113207547169811)^2)

245283019)^2)

245283019)^2)

0381)

792453))^2

115169 -42612 53

GCD 1 -804 53

LCM 14 x y

-5 -15 -2.85714

1 3 2.285714 53 1369

-5.39623 -0.113213 9 4

4 12 4.857143

5.84 17.52 6.434286

ius line has 5.84 17.52 6.434286

dius line: 266 15.16981 9

b 2809

7 53

r=((x_0-x_1)^2 + (y_0-y_1)^2)

nt point r=((h-x_1)^2 + (k-y_1)^2)

r=((-4- (-286 / 53))^2 + (-5- (-42/371))^2)

r=((-212/53 + 286 / 53)^2 + (-1855/371 + 42/371)^2)

r=((74/53)^2 + (-1813/371)^2) 5476/2809 + 3286969

r=(5476/2809 + 3286969/137641) 137641 49

-15-14-13-12-11-10

-9-8-7-6-5-4-3-2-101234567

89

101112131415

-15-14-13-12-11-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 1011 1213 1415


23/51

286 / 53 r=( (5476/2809)(49/49) + 3286969/137641) 2809

42/371 r=(268324/137641 + 3286969/137641) 2809

+ (10/7)(53/53) r=(3555293/137641) 268324 3286969

+ 530/371 r=(3555293/137641) 3555293 1885.548

r=( (49)(72557)/137641) 72557 2809

r=7/371 (72557) 0.018868 5.082341 72557

(x -(-4))^2 + (y - (-5))^2 = r^2 (74*74*49)+(1813*18 371(x -(-4))^2 + (y - (-5))^2 = (7/371 (72557))^2


24/51


25/51


26/51


27/51


28/51


29/51


30/51

r=((x_0-x_1)^2 + (y_0-y_1)^2)

r=((h-x_1)^2 + (k-y_1)^2)

r=((-4-6)^2 + (1--1)^2)

r=((-4-6)^2 + (1--1)^2)

r=((-10)^2 + (2)^2)

r=((-10)^2 + (2)^2)

r=(100 + 4)r=(104)

(x -2)^2+ (y - 5)^2= r^2

(x -(-4))^2 + (y - 1)^2 = ((104))^2

(x + 4)^2 + (y - 1)^2 = 104

x^2 -8x + 16 + y^2 +2y + 1 = 104

x^2 + y^2 -8x +2y + 16 + 1 = 104

x^2 + y^2 -8x +2y + 17 = 104

x^2 + y^2 -8x +2y = 104-17

x^2 + y^2 -8x +2y = 87

137641


31/51

5.082341

53

371


32/51

x^2 y^2 x y n a + +

5 5 10 -5 3 0 5x^2 5y^2 10x

2.2360679 2.23606797749979y

h=(-10/5)(1/2)

h=-10/10

h=-1 5

k=(5/5)(1/2)k=1/2

k=0.5 -2.5

5x^2 + 5y^2 + 10x - 5y + 3 = 0

5 1/5[ 5x^2 + 5y^2 + 10x - 5y + 3 = 0

5 1/5 x^2 + y^2 + 2 - 1 + 3/5 = 0

x^2 + y^2 + 2 - 1 + 3/5 = 0

5x^2 + 5y^2 + 10x - 5y = 0 - 3

5x^2 + 5y^2 + 10x - 5y = -3

5x^2 + 10x + 5y^2 - 5y = -3

(5x^2 + 10x) + (5y^2 - 5y) = -3

(5x^2 + 10x + 25) + (5y^2 - 5y + 6.

(5x^2 + 10x + 25) + (5y^2 - 5y + 6.

(2.23606797749979x + 5)^2 + (2.2

r = (28.25)

r =5.31507290636732


33/51

- + + - 3

5y 3 0

1

h=-4/2 65

h=-2

k=6/2

k=3x^2 + y^2 + 4x - 6y - 12 = 0

x^2 + y^2 + 4x - 6y = 0 - 12

x^2 + y^2 + 4x - 6y = 0 + 12

] x^2 + y^2 + 4x - 6y = 12

x^2 + 4x + y^2 - 6y = 12

(x^2 + 4x) + (y^2 - 6y) = 12

(x^2 + 4x + 4) + (y^2 - 6y + 9) = 12 + 4 + 9

(x^2 + 4x + 4) + (y^2 - 6y + 9) = 25

(x + 2)^2 + (y - 3)^2 = 25

r = (25)

5) = -3 + 2 r =5

5) = 28.25

3606797749979y - 3)^2 = 28.25


34/51

h k r (x - h)2 + (y - k)2 = r2 Radius r=((x_0-x_1)^2 + (y_0-y_1)^2)

-2 3 5 (x - )^2 r=((h-x_1)^2 + (k-y_1)^2)

(y - r=((-2--5.39622641509434)^2 + (3--0.

-1 r=((-2--5.39622641509434)^2 + (3--0.

r=((3.39622641509434)^2 + (3.11320

1 0 3 3 r=((3.39622641509434)^2 + (3.11320

2 0.017453 2.999238 3.087262 r=(11.5343538625846 + 9.6920612313 0.034907 2.996954 3.174497 r=(21.2264150 (21.2264150943396)

4 0.05236 2.993148 3.26168 r = 4.60721337625463

5 0.069813 2.98782 3.348782 (x -(-2))^2 + (y - 3)^2 = r^2

6 0.087266 2.980973 3.435779 (x -(-2))^2 + (y - 3)^2 = ((21.22641509

7 0.10472 2.972609 3.522642

8 0.122173 2.962731 3.609347 Circle (x -(-2))^2 + (y - 3)^2 = 5^2

9 0.139626 2.95134 3.695866 (x + 2)^2 + (y - 3)^2 = 25

10 0.15708 2.938442 3.782172 x^2 -4x + 4 + y^2 +6y + 9 = 25

11 0.174533 2.924039 3.868241 x^2 + y^2 -4x +6y + 4 + 9 = 25

12 0.191986 2.908136 3.954045 x^2 + y^2 -4x +6y + 13 = 25

13 0.20944 2.890738 4.039558 x^2 + y^2 -4x +6y = 25-13

14 0.226893 2.87185 4.124755 x^2 + y^2 -4x +6y = 12

15 0.244346 2.851479 4.209609 X_1 y_1

16 0.261799 2.829629 4.294095 -5.39623 -0.113207547

17 0.279253 2.806308 4.378187

18 0.296706 2.781524 4.461859 4.607213

19 0.314159 2.755283 4.545085 2 -7 10

20 0.331613 2.727593 4.627841 2x-7y + 10 = 0

21 0.349066 2.698463 4.710101 -7y = -2x-10

22 0.366519 2.667902 4.79184 y = -2/-7 x-10/-7 -2/-7 x-10/ -0.28571

23 0.383972 2.635919 4.873033 -7/-7 y = 2/7 x+10/724 0.401426 2.602524 4.953656 y = 2/7 x+10/7

25 0.418879 2.567727 5.033683 slope of tangent line

26 0.436332 2.531539 5.113091 m_t = -2/-7 2/-7

27 0.453786 2.49397 5.191856 tangent line is perpendicular to radius line thus rad

28 0.471239 2.455033 5.269952 m_r = -7/2

29 0.488692 2.414738 5.347358 substituting the center to get the equation of the r

30 0.506145 2.373099 5.424048 y=mx+b y=mx+b

31 0.523599 2.330127 5.5 y=-7/2 x+b y=4/3 x+b

32 0.541052 2.285837 5.57519 3=(-7/2)(-2)+b -7/2 x +-14 7=(4/3)(-1)

33 0.558505 2.24024 5.649596 3=14/2 +b -35 7=-4/3+b

34 0.575959 2.193353 5.723195 3-14/2=b 7+4/3=b

35 0.593412 2.145188 5.795965 b = -8/2 b=25/3

36 0.610865 2.09576 5.867882 y=-7/2 x+-8/2

37 0.628319 2.045085 5.938926 solving for the system of equations to get the tang

38 0.645772 1.993178 6.009075 -7/2 x+-8/2 = -2/-7 x-10/-7

39 0.663225 1.940054 6.078307 -49 x+-56 = 4 x20

40 0.680678 1.88573 6.146602 -49 x -4 x = 20+56

41 0.698132 1.830222 6.213938 -53 x = 76 -5.39623


35/51

42 0.715585 1.773548 6.280295 x = -76 / 53 x -76 / 53

43 0.733038 1.715724 6.345653 y = 2/7 x+10/7 y -42/371

44 0.750492 1.656769 6.409992 y = (2/7) (-76 / 53)+10/7 y=-572/371

45 0.767945 1.596699 6.473292 y = -2.86792452830189/7+10/7 y=-572/371

46 0.785398 1.535534 6.535534 y = 7.13207547169811/7 y=-42/371

47 0.802851 1.473292 6.596699 y = 1.0188679245283

48 0.820305 1.409992 6.656769 tangent point is at (-76 / 53 , -42/371)49 0.837758 1.345653 6.715724

50 0.855211 1.280295 6.773548

51 0.872665 1.213938 6.830222

52 0.890118 1.146602 6.88573

53 0.907571 1.078307 6.940054

54 0.925025 1.009075 6.993178

55 0.942478 0.938926 7.045085

56 0.959931 0.867882 7.09576

57 0.977384 0.795965 7.145188

58 0.994838 0.723195 7.193353

59 1.012291 0.649596 7.24024

60 1.029744 0.57519 7.285837

61 1.047198 0.5 7.330127

62 1.064651 0.424048 7.373099

63 1.082104 0.347358 7.414738

64 1.099557 0.269952 7.455033

65 1.117011 0.191856 7.49397

66 1.134464 0.113091 7.531539

67 1.151917 0.033683 7.567727

68 1.169371 -0.04634 7.602524

69 1.186824 -0.12697 7.63591970 1.204277 -0.20816 7.667902

71 1.22173 -0.2899 7.698463

72 1.239184 -0.37216 7.727593

73 1.256637 -0.45492 7.755283

74 1.27409 -0.53814 7.781524

75 1.291544 -0.62181 7.806308

76 1.308997 -0.7059 7.829629

77 1.32645 -0.79039 7.851479

78 1.343904 -0.87524 7.87185

79 1.361357 -0.96044 7.890738

80 1.37881 -1.04596 7.908136

81 1.396263 -1.13176 7.924039

82 1.413717 -1.21783 7.938442

83 1.43117 -1.30413 7.95134

84 1.448623 -1.39065 7.962731

85 1.466077 -1.47736 7.972609

86 1.48353 -1.56422 7.980973

87 1.500983 -1.65122 7.98782

88 1.518436 -1.73832 7.993148


36/51

89 1.53589 -1.8255 7.996954

90 1.553343 -1.91274 7.999238

91 1.570796 -2 8

92 1.58825 -2.08726 7.999238

93 1.605703 -2.1745 7.996954

94 1.623156 -2.26168 7.993148

95 1.640609 -2.34878 7.9878296 1.658063 -2.43578 7.980973

97 1.675516 -2.52264 7.972609

98 1.692969 -2.60935 7.962731

99 1.710423 -2.69587 7.95134

100 1.727876 -2.78217 7.938442

101 1.745329 -2.86824 7.924039

102 1.762783 -2.95404 7.908136

103 1.780236 -3.03956 7.890738

104 1.797689 -3.12476 7.87185

105 1.815142 -3.20961 7.851479

106 1.832596 -3.2941 7.829629

107 1.850049 -3.37819 7.806308

108 1.867502 -3.46186 7.781524

109 1.884956 -3.54508 7.755283

110 1.902409 -3.62784 7.727593

111 1.919862 -3.7101 7.698463

112 1.937315 -3.79184 7.667902

113 1.954769 -3.87303 7.635919

114 1.972222 -3.95366 7.602524

115 1.989675 -4.03368 7.567727

116 2.007129 -4.11309 7.531539117 2.024582 -4.19186 7.49397

118 2.042035 -4.26995 7.455033

119 2.059489 -4.34736 7.414738

120 2.076942 -4.42405 7.373099

121 2.094395 -4.5 7.330127

122 2.111848 -4.57519 7.285837

123 2.129302 -4.6496 7.24024

124 2.146755 -4.7232 7.193353

125 2.164208 -4.79596 7.145188

126 2.181662 -4.86788 7.09576

127 2.199115 -4.93893 7.045085

128 2.216568 -5.00908 6.993178

129 2.234021 -5.07831 6.940054

130 2.251475 -5.1466 6.88573

131 2.268928 -5.21394 6.830222

132 2.286381 -5.2803 6.773548

133 2.303835 -5.34565 6.715724

134 2.321288 -5.40999 6.656769

135 2.338741 -5.47329 6.596699


37/51

136 2.356194 -5.53553 6.535534

137 2.373648 -5.5967 6.473292

138 2.391101 -5.65677 6.409992

139 2.408554 -5.71572 6.345653

140 2.426008 -5.77355 6.280295

141 2.443461 -5.83022 6.213938

142 2.460914 -5.88573 6.146602143 2.478368 -5.94005 6.078307

144 2.495821 -5.99318 6.009075

145 2.513274 -6.04508 5.938926

146 2.530727 -6.09576 5.867882

147 2.548181 -6.14519 5.795965

148 2.565634 -6.19335 5.723195

149 2.583087 -6.24024 5.649596

150 2.600541 -6.28584 5.57519

151 2.617994 -6.33013 5.5

152 2.635447 -6.3731 5.424048

153 2.6529 -6.41474 5.347358

154 2.670354 -6.45503 5.269952

155 2.687807 -6.49397 5.191856

156 2.70526 -6.53154 5.113091

157 2.722714 -6.56773 5.033683

158 2.740167 -6.60252 4.953656

159 2.75762 -6.63592 4.873033

160 2.775074 -6.6679 4.79184

161 2.792527 -6.69846 4.710101

162 2.80998 -6.72759 4.627841

163 2.827433 -6.75528 4.545085164 2.844887 -6.78152 4.461859

165 2.86234 -6.80631 4.378187

166 2.879793 -6.82963 4.294095

167 2.897247 -6.85148 4.209609

168 2.9147 -6.87185 4.124755

169 2.932153 -6.89074 4.039558

170 2.949606 -6.90814 3.954045

171 2.96706 -6.92404 3.868241

172 2.984513 -6.93844 3.782172

173 3.001966 -6.95134 3.695866

174 3.01942 -6.96273 3.609347

175 3.036873 -6.97261 3.522642

176 3.054326 -6.98097 3.435779

177 3.071779 -6.98782 3.348782

178 3.089233 -6.99315 3.26168

179 3.106686 -6.99695 3.174497

180 3.124139 -6.99924 3.087262

181 3.141593 -7 3

182 3.159046 -6.99924 2.912738


38/51

183 3.176499 -6.99695 2.825503

184 3.193953 -6.99315 2.73832

185 3.211406 -6.98782 2.651218

186 3.228859 -6.98097 2.564221

187 3.246312 -6.97261 2.477358

188 3.263766 -6.96273 2.390653

189 3.281219 -6.95134 2.304134190 3.298672 -6.93844 2.217828

191 3.316126 -6.92404 2.131759

192 3.333579 -6.90814 2.045955

193 3.351032 -6.89074 1.960442

194 3.368485 -6.87185 1.875245

195 3.385939 -6.85148 1.790391

196 3.403392 -6.82963 1.705905

197 3.420845 -6.80631 1.621813

198 3.438299 -6.78152 1.538141

199 3.455752 -6.75528 1.454915

200 3.473205 -6.72759 1.372159

201 3.490659 -6.69846 1.289899

202 3.508112 -6.6679 1.20816

203 3.525565 -6.63592 1.126967

204 3.543018 -6.60252 1.046344

205 3.560472 -6.56773 0.966317

206 3.577925 -6.53154 0.886909

207 3.595378 -6.49397 0.808144

208 3.612832 -6.45503 0.730048

209 3.630285 -6.41474 0.652642

210 3.647738 -6.3731 0.575952211 3.665191 -6.33013 0.5

212 3.682645 -6.28584 0.42481

213 3.700098 -6.24024 0.350404

214 3.717551 -6.19335 0.276805

215 3.735005 -6.14519 0.204035

216 3.752458 -6.09576 0.132118

217 3.769911 -6.04508 0.061074

218 3.787364 -5.99318 -0.00908

219 3.804818 -5.94005 -0.07831

220 3.822271 -5.88573 -0.1466

221 3.839724 -5.83022 -0.21394

222 3.857178 -5.77355 -0.2803

223 3.874631 -5.71572 -0.34565

224 3.892084 -5.65677 -0.40999

225 3.909538 -5.5967 -0.47329

226 3.926991 -5.53553 -0.53553

227 3.944444 -5.47329 -0.5967

228 3.961897 -5.40999 -0.65677

229 3.979351 -5.34565 -0.71572


39/51

230 3.996804 -5.2803 -0.77355

231 4.014257 -5.21394 -0.83022

232 4.031711 -5.1466 -0.88573

233 4.049164 -5.07831 -0.94005

234 4.066617 -5.00908 -0.99318

235 4.08407 -4.93893 -1.04508

236 4.101524 -4.86788 -1.09576237 4.118977 -4.79596 -1.14519

238 4.13643 -4.7232 -1.19335

239 4.153884 -4.6496 -1.24024

240 4.171337 -4.57519 -1.28584

241 4.18879 -4.5 -1.33013

242 4.206243 -4.42405 -1.3731

243 4.223697 -4.34736 -1.41474

244 4.24115 -4.26995 -1.45503

245 4.258603 -4.19186 -1.49397

246 4.276057 -4.11309 -1.53154

247 4.29351 -4.03368 -1.56773

248 4.310963 -3.95366 -1.60252

249 4.328417 -3.87303 -1.63592

250 4.34587 -3.79184 -1.6679

251 4.363323 -3.7101 -1.69846

252 4.380776 -3.62784 -1.72759

253 4.39823 -3.54508 -1.75528

254 4.415683 -3.46186 -1.78152

255 4.433136 -3.37819 -1.80631

256 4.45059 -3.2941 -1.82963

257 4.468043 -3.20961 -1.85148258 4.485496 -3.12476 -1.87185

259 4.502949 -3.03956 -1.89074

260 4.520403 -2.95404 -1.90814

261 4.537856 -2.86824 -1.92404

262 4.555309 -2.78217 -1.93844

263 4.572763 -2.69587 -1.95134

264 4.590216 -2.60935 -1.96273

265 4.607669 -2.52264 -1.97261

266 4.625123 -2.43578 -1.98097

267 4.642576 -2.34878 -1.98782

268 4.660029 -2.26168 -1.99315

269 4.677482 -2.1745 -1.99695

270 4.694936 -2.08726 -1.99924

271 4.712389 -2 -2

272 4.729842 -1.91274 -1.99924

273 4.747296 -1.8255 -1.99695

274 4.764749 -1.73832 -1.99315

275 4.782202 -1.65122 -1.98782

276 4.799655 -1.56422 -1.98097


40/51

277 4.817109 -1.47736 -1.97261

278 4.834562 -1.39065 -1.96273

279 4.852015 -1.30413 -1.95134

280 4.869469 -1.21783 -1.93844

281 4.886922 -1.13176 -1.92404

282 4.904375 -1.04596 -1.90814

283 4.921828 -0.96044 -1.89074284 4.939282 -0.87524 -1.87185

285 4.956735 -0.79039 -1.85148

286 4.974188 -0.7059 -1.82963

287 4.991642 -0.62181 -1.80631

288 5.009095 -0.53814 -1.78152

289 5.026548 -0.45492 -1.75528

290 5.044002 -0.37216 -1.72759

291 5.061455 -0.2899 -1.69846

292 5.078908 -0.20816 -1.6679

293 5.096361 -0.12697 -1.63592

294 5.113815 -0.04634 -1.60252

295 5.131268 0.033683 -1.56773

296 5.148721 0.113091 -1.53154

297 5.166175 0.191856 -1.49397

298 5.183628 0.269952 -1.45503

299 5.201081 0.347358 -1.41474

300 5.218534 0.424048 -1.3731

301 5.235988 0.5 -1.33013

302 5.253441 0.57519 -1.28584

303 5.270894 0.649596 -1.24024

304 5.288348 0.723195 -1.19335305 5.305801 0.795965 -1.14519

306 5.323254 0.867882 -1.09576

307 5.340708 0.938926 -1.04508

308 5.358161 1.009075 -0.99318

309 5.375614 1.078307 -0.94005

310 5.393067 1.146602 -0.88573

311 5.410521 1.213938 -0.83022

312 5.427974 1.280295 -0.77355

313 5.445427 1.345653 -0.71572

314 5.462881 1.409992 -0.65677

315 5.480334 1.473292 -0.5967

316 5.497787 1.535534 -0.53553

317 5.51524 1.596699 -0.47329

318 5.532694 1.656769 -0.40999

319 5.550147 1.715724 -0.34565

320 5.5676 1.773548 -0.2803

321 5.585054 1.830222 -0.21394

322 5.602507 1.88573 -0.1466

323 5.61996 1.940054 -0.07831


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324 5.637413 1.993178 -0.00908

325 5.654867 2.045085 0.061074

326 5.67232 2.09576 0.132118

327 5.689773 2.145188 0.204035

328 5.707227 2.193353 0.276805

329 5.72468 2.24024 0.350404

330 5.742133 2.285837 0.42481331 5.759587 2.330127 0.5

332 5.77704 2.373099 0.575952

333 5.794493 2.414738 0.652642

334 5.811946 2.455033 0.730048

335 5.8294 2.49397 0.808144

336 5.846853 2.531539 0.886909

337 5.864306 2.567727 0.966317

338 5.88176 2.602524 1.046344

339 5.899213 2.635919 1.126967

340 5.916666 2.667902 1.20816

341 5.934119 2.698463 1.289899

342 5.951573 2.727593 1.372159

343 5.969026 2.755283 1.454915

344 5.986479 2.781524 1.538141

345 6.003933 2.806308 1.621813

346 6.021386 2.829629 1.705905

347 6.038839 2.851479 1.790391

348 6.056293 2.87185 1.875245

349 6.073746 2.890738 1.960442

350 6.091199 2.908136 2.045955

351 6.108652 2.924039 2.131759352 6.126106 2.938442 2.217828

353 6.143559 2.95134 2.304134

354 6.161012 2.962731 2.390653

355 6.178466 2.972609 2.477358

356 6.195919 2.980973 2.564221

357 6.213372 2.98782 2.651218

358 6.230825 2.993148 2.73832

359 6.248279 2.996954 2.825503

360 6.265732 2.999238 2.912738

361 6.283185 3 3


42/51

13207547169811)^2)

13207547169811)^2)

54716981)^2)

54716981)^2)

5507)

3396))^2

115169 -42612 53

GCD 1 -804 53

LCM 14 x y

-5 -15 -2.85714

1 3 2.285714 53 1369

-5.39623 -0.113213 9 4

4 12 4.857143

5.84 17.52 6.434286

ius line has 5.84 17.52 6.434286

dius line: 266 15.16981 9

b 2809

7 53

r=((x_0-x_1)^2 + (y_0-y_1)^2)

nt point r=((h-x_1)^2 + (k-y_1)^2)

r=((-2- (-76 / 53))^2 + (3- (-42/371))^2)

r=((-106/53 + 76 / 53)^2 + (1113/371 + 42/371)^2)

r=((180/53)^2 + (1155/371)^2) 5476/2809 + 3286969

r=(5476/2809 + 3286969/137641) 137641 49

-15-14-13-12-11-10

-9-8-7-6-5-4-3-2-101234567

89

101112131415

-15-14-13-12-11-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 1011 1213 1415


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76 / 53 r=( (5476/2809)(49/49) + 3286969/137641) 2809

42/371 r=(268324/137641 + 3286969/137641) 2809

+ (10/7)(53/53) r=(3555293/137641) 268324 3286969

+ 530/371 r=(3555293/137641) 3555293 1885.548

r=( (49)(72557)/137641) 72557 2809

r=7/371 (72557) 0.018868 5.082341 72557

(x -(-2))^2 + (y - 3)^2 = r^2 (74*74*49)+(1813*18 371(x -(-2))^2 + (y - 3)^2 = (7/371 (72557))^2


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45/51


46/51


47/51


48/51


49/51


50/51

r=((x_0-x_1)^2 + (y_0-y_1)^2)

r=((h-x_1)^2 + (k-y_1)^2)

r=((-4-6)^2 + (1--1)^2)

r=((-4-6)^2 + (1--1)^2)

r=((-10)^2 + (2)^2)

r=((-10)^2 + (2)^2)

r=(100 + 4)r=(104)

(x -2)^2+ (y - 5)^2= r^2

(x -(-4))^2 + (y - 1)^2 = ((104))^2

(x + 4)^2 + (y - 1)^2 = 104

x^2 -8x + 16 + y^2 +2y + 1 = 104

x^2 + y^2 -8x +2y + 16 + 1 = 104

x^2 + y^2 -8x +2y + 17 = 104

x^2 + y^2 -8x +2y = 104-17

x^2 + y^2 -8x +2y = 87

137641


51/51

5.082341

53

371

geom charts - exercise 4

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