x2 t03 03 parameters, ellipse (2012)
TRANSCRIPT
![Page 1: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/1.jpg)
Conics & Parametersy
xa-a
a
-a
1) Circle
222 ayx
![Page 2: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/2.jpg)
Conics & Parametersy
xa-a
a
-a
1) Circle
222 ayx
yxP ,
![Page 3: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/3.jpg)
Conics & Parametersy
xa-a
a
-a
1) Circle
yxP ,a
x
222 ayx
cosax
![Page 4: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/4.jpg)
Conics & Parametersy
xa-a
a
-a
1) Circle
yxP ,a
x
222 ayx
cosax
cosax
![Page 5: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/5.jpg)
Conics & Parametersy
xa-a
a
-a
1) Circle
yxP ,a
x
cosax
cosax
y
sinay
sinay
222 ayx
![Page 6: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/6.jpg)
Conics & Parametersy
xa-a
a
-a
1) Circle
yxP ,a
x
cosax
cosax
y
sinay
sinay
222 ayx
Proof:
2
222
222222
sincossincos
aa
aayx
![Page 7: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/7.jpg)
2) Ellipse y
xa-a
b
-b
yxP ,
![Page 8: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/8.jpg)
2) Ellipse y
xa-a
b
-b222 ayx
yxP ,
![Page 9: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/9.jpg)
2) Ellipse y
xa-a
b
-b222 ayx
yxP ,
x
![Page 10: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/10.jpg)
2) Ellipse y
xa-a
b
-b222 ayx
yxP ,
cosax
cosax
x
![Page 11: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/11.jpg)
2) Ellipse y
xa-a
b
-b222 ayx
yxP ,
cosax
cosax
xy
![Page 12: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/12.jpg)
2) Ellipse y
xa-a
b
-b222 ayx
yxP ,
cosax
cosax
xy
sinby
sinby
![Page 13: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/13.jpg)
2) Ellipse y
xa-a
b
-b
yxP ,
xy
222 ayx
222 byx
cosax
cosax
sinby
sinby
Proof:
1sincos
sincos
22
2
22
2
22
2
2
2
2
b
ba
aby
ax
![Page 14: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/14.jpg)
Equation of Tangent and Normaly
xa-a
b
-b
11, yxP
12
2
2
2
by
ax
![Page 15: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/15.jpg)
Equation of Tangent and Normaly
xa-a
b
-b
11, yxP
12
2
2
2
by
ax
02222
dxdy
by
ax
dxdy
dydf
dxdf
![Page 16: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/16.jpg)
Equation of Tangent and Normaly
xa-a
b
-b
11, yxP
12
2
2
2
by
ax
02222
dxdy
by
ax
dxdy
dydf
dxdf
yaxb
dxdy
ax
dxdy
by
2
2
2222
![Page 17: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/17.jpg)
Equation of Tangent and Normaly
xa-a
b
-b
11, yxP
12
2
2
2
by
ax
02222
dxdy
by
ax
dxdy
dydf
dxdf
yaxb
dxdy
ax
dxdy
by
2
2
2222
11,at yxP
12
12
yaxb
dxdy
![Page 18: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/18.jpg)
y
xa-a
b
-b
11, yxP
tangent:
11
21
2
1 xxyaxbyy
![Page 19: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/19.jpg)
y
xa-a
b
-b
11, yxP
tangent:
11
21
2
1 xxyaxbyy
21
221
21
21
2
21
21
221
21
2
yaxbyyaxxb
xbxxbyayya
![Page 20: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/20.jpg)
y
xa-a
b
-b
11, yxP
tangent:
11
21
2
1 xxyaxbyy
21
221
21
21
2
21
21
221
21
2
yaxbyyaxxb
xbxxbyayya
2
21
2
21
21
21
by
ax
byy
axx
![Page 21: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/21.jpg)
y
xa-a
b
-b
11, yxP
tangent:
11
21
2
1 xxyaxbyy
21
221
21
21
2
21
21
221
21
2
yaxbyyaxxb
xbxxbyayya
2
21
2
21
21
21
by
ax
byy
axx
121
21
byy
axx
![Page 22: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/22.jpg)
y
xa-a
b
-b
11, yxP
tangent:
11
21
2
1 xxyaxbyy
21
221
21
21
2
21
21
221
21
2
yaxbyyaxxb
xbxxbyayya
2
21
2
21
21
21
by
ax
byy
axx
121
21
byy
axx
normal:
11
21
2
1 xxxbyayy
![Page 23: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/23.jpg)
y
xa-a
b
-b
11, yxP
tangent:
11
21
2
1 xxyaxbyy
21
221
21
21
2
21
21
221
21
2
yaxbyyaxxb
xbxxbyayya
2
21
2
21
21
21
by
ax
byy
axx
121
21
byy
axx
normal:
11
21
2
1 xxxbyayy
112
112
12
12
112
12
112
12
yxbyxayxbxya
yxaxyayxbyxb
![Page 24: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/24.jpg)
y
xa-a
b
-b
11, yxP
tangent:
11
21
2
1 xxyaxbyy
21
221
21
21
2
21
21
221
21
2
yaxbyyaxxb
xbxxbyayya
2
21
2
21
21
21
by
ax
byy
axx
121
21
byy
axx
normal:
11
21
2
1 xxxbyayy
112
112
12
12
112
12
112
12
yxbyxayxbxya
yxaxyayxbyxb
22
1
2
1
2
bay
ybx
xa
![Page 25: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/25.jpg)
Using Parametric Coordinates; sin,cosat baP
![Page 26: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/26.jpg)
Using Parametric Coordinates; sin,cosat baP
sincos
sincos
2
2
ab
baab
dxdy
![Page 27: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/27.jpg)
Using Parametric Coordinates; sin,cosat baP
sincos
sincos
2
2
ab
baab
dxdy
tangent:
cos
sincossin ax
abby
![Page 28: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/28.jpg)
Using Parametric Coordinates; sin,cosat baP
sincos
sincos
2
2
ab
baab
dxdy
tangent:
cos
sincossin ax
abby
22
22
cossinsincoscoscossinsin
ababaybxabbxabay
![Page 29: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/29.jpg)
Using Parametric Coordinates; sin,cosat baP
sincos
sincos
2
2
ab
baab
dxdy
tangent:
cos
sincossin ax
abby
22
22
cossinsincoscoscossinsin
ababaybxabbxabay
22 cossinsincos
by
ax
![Page 30: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/30.jpg)
Using Parametric Coordinates; sin,cosat baP
sincos
sincos
2
2
ab
baab
dxdy
tangent:
cos
sincossin ax
abby
22
22
cossinsincoscoscossinsin
ababaybxabbxabay
22 cossinsincos
by
ax
1sincos
by
ax
![Page 31: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/31.jpg)
Using Parametric Coordinates; sin,cosat baP
sincos
sincos
2
2
ab
baab
dxdy
tangent:
cos
sincossin ax
abby
22
22
cossinsincoscoscossinsin
ababaybxabbxabay
22 cossinsincos
by
ax
1sincos
by
ax
normal:
cos
cossinsin ax
baby
![Page 32: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/32.jpg)
Using Parametric Coordinates; sin,cosat baP
sincos
sincos
2
2
ab
baab
dxdy
tangent:
cos
sincossin ax
abby
22
22
cossinsincoscoscossinsin
ababaybxabbxabay
22 cossinsincos
by
ax
1sincos
by
ax
normal:
cos
cossinsin ax
baby
cossin cossin
cossinsin cossincos
22
2
2
babyax
aaxbby
![Page 33: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/33.jpg)
Using Parametric Coordinates; sin,cosat baP
sincos
sincos
2
2
ab
baab
dxdy
tangent:
cos
sincossin ax
abby
22
22
cossinsincoscoscossinsin
ababaybxabbxabay
22 cossinsincos
by
ax
1sincos
by
ax
normal:
cos
cossinsin ax
baby
cossin cossin
cossinsin cossincos
22
2
2
babyax
aaxbby
22
sincosbabyax
![Page 34: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/34.jpg)
For ellipse 12
2
2
2
by
ax
11,at tangent yx
121
21
byy
axx
![Page 35: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/35.jpg)
For ellipse 12
2
2
2
by
ax
11,at tangent yx
121
21
byy
axx
11,at normal yx
22
1
2
1
2
bay
ybx
xa
![Page 36: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/36.jpg)
For ellipse 12
2
2
2
by
ax
11,at tangent yx
121
21
byy
axx
11,at normal yx
22
1
2
1
2
bay
ybx
xa
sin,cosat tangent ba
1sincos
by
ax
![Page 37: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/37.jpg)
For ellipse 12
2
2
2
by
ax
11,at tangent yx
121
21
byy
axx
11,at normal yx
22
1
2
1
2
bay
ybx
xa
sin,cosat tangent ba sin,cosat normal ba
1sincos
by
ax 22
sincosbabyax
![Page 38: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/38.jpg)
e.g. (i)
23,2point at the
116 ellipse theo tangent t theofequation theFind 2
2
yx
![Page 39: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/39.jpg)
e.g. (i)
23,2point at the
116 ellipse theo tangent t theofequation theFind 2
2
yx
yx
dxdydxdyyx
16
028
![Page 40: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/40.jpg)
e.g. (i)
23,2point at the
116 ellipse theo tangent t theofequation theFind 2
2
yx
yx
dxdydxdyyx
16
028
341
2316
2 ,2
3,2at
dxdy
dxdy
![Page 41: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/41.jpg)
e.g. (i)
23,2point at the
116 ellipse theo tangent t theofequation theFind 2
2
yx
yx
dxdydxdyyx
16
028
341
2316
2 ,2
3,2at
dxdy
dxdy
234
123 xy
![Page 42: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/42.jpg)
e.g. (i)
23,2point at the
116 ellipse theo tangent t theofequation theFind 2
2
yx
yx
dxdydxdyyx
16
028
341
2316
2 ,2
3,2at
dxdy
dxdy
234
123 xy
08342634
yxxy
![Page 43: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/43.jpg)
(ii)
6point at the
sin,2cosellipsethetonormaltheofequation theFind
yx
![Page 44: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/44.jpg)
(ii)
6point at the
sin,2cosellipsethetonormaltheofequation theFind
yx
xfy sin
xfxfdxdy cos
![Page 45: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/45.jpg)
(ii)
6point at the
sin,2cosellipsethetonormaltheofequation theFind
yx
xfy sin
xfxfdxdy cos
xfy cos
xfxfdxdy sin
![Page 46: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/46.jpg)
(ii)
6point at the
sin,2cosellipsethetonormaltheofequation theFind
yx
xfy sin
xfxfdxdy cos
xfy cos
xfxfdxdy sin
cos2x
sin2ddx
![Page 47: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/47.jpg)
(ii)
6point at the
sin,2cosellipsethetonormaltheofequation theFind
yx
xfy sin
xfxfdxdy cos
xfy cos
xfxfdxdy sin
cos2x
sin2ddx
siny
cosddy
![Page 48: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/48.jpg)
(ii)
6point at the
sin,2cosellipsethetonormaltheofequation theFind
yx
xfy sin
xfxfdxdy cos
xfy cos
xfxfdxdy sin
cos2x
sin2ddx
siny
cosddy
sin2cos
dxd
ddy
dxdy
![Page 49: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/49.jpg)
(ii)
6point at the
sin,2cosellipsethetonormaltheofequation theFind
yx
xfy sin
xfxfdxdy cos
xfy cos
xfxfdxdy sin
cos2x
sin2ddx
siny
cosddy
sin2cos
dxd
ddy
dxdy
23
123
,6
at
dxdy
![Page 50: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/50.jpg)
(ii)
6point at the
sin,2cosellipsethetonormaltheofequation theFind
yx
xfy sin
xfxfdxdy cos
xfy cos
xfxfdxdy sin
cos2x
sin2ddx
siny
cosddy
sin2cos
dxd
ddy
dxdy
23
123
,6
at
dxdy 3
32
21
xy
![Page 51: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/51.jpg)
(ii)
6point at the
sin,2cosellipsethetonormaltheofequation theFind
yx
xfy sin
xfxfdxdy cos
xfy cos
xfxfdxdy sin
cos2x
sin2ddx
siny
cosddy
sin2cos
dxd
ddy
dxdy
23
123
,6
at
dxdy 3
32
21
xy
033324344332
yxxy
![Page 52: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/52.jpg)
(iii)
22222
2
2
2
then ,1
ellipsetheotangent taisif that Show
kbmaby
ax
kmxy
![Page 53: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/53.jpg)
(iii)
22222
2
2
2
then ,1
ellipsetheotangent taisif that Show
kbmaby
ax
kmxy
cosax
sinaddx
sinby
cosbddy
sincos
ab
dxdy
![Page 54: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/54.jpg)
(iii)
22222
2
2
2
then ,1
ellipsetheotangent taisif that Show
kbmaby
ax
kmxy
cosax
sinaddx
sinby
cosbddy
sincos
ab
dxdy
mdxdykmxy hen tangent ta is If
![Page 55: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/55.jpg)
(iii)
22222
2
2
2
then ,1
ellipsetheotangent taisif that Show
kbmaby
ax
kmxy
cosax
sinaddx
sinby
cosbddy
sincos
ab
dxdy
mdxdykmxy hen tangent ta is If
sincos i.e.
abm
![Page 56: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/56.jpg)
(iii)
22222
2
2
2
then ,1
ellipsetheotangent taisif that Show
kbmaby
ax
kmxy
cosax
sinaddx
sinby
cosbddy
sincos
ab
dxdy
mdxdykmxy hen tangent ta is If
sincos i.e.
abm
)1(0cossincossin
bam
bam
![Page 57: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/57.jpg)
(iii)
22222
2
2
2
then ,1
ellipsetheotangent taisif that Show
kbmaby
ax
kmxy
cosax
sinaddx
sinby
cosbddy
sincos
ab
dxdy
mdxdykmxy hen tangent ta is If
sincos i.e.
abm
)1(0cossincossin
bam
bam
then;sin,cosat ellipsemeets tangent If bakamb cossin
![Page 58: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/58.jpg)
(iii)
22222
2
2
2
then ,1
ellipsetheotangent taisif that Show
kbmaby
ax
kmxy
cosax
sinaddx
sinby
cosbddy
sincos
ab
dxdy
mdxdykmxy hen tangent ta is If
sincos i.e.
abm
)1(0cossincossin
bam
bam
then;sin,cosat ellipsemeets tangent If bakamb cossin)2(sincos kbam
![Page 59: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/59.jpg)
0coscossin2sin:1 222222 babmma
2222222 sincossin2cos:2 kbabmma
(+)
![Page 60: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/60.jpg)
0coscossin2sin:1 222222 babmma
2222222 sincossin2cos:2 kbabmma
(+)
22222222 cossincossin kbma
![Page 61: X2 t03 03 parameters, ellipse (2012)](https://reader033.vdocuments.us/reader033/viewer/2022052700/55a1e5291a28ab85508b46f5/html5/thumbnails/61.jpg)
0coscossin2sin:1 222222 babmma
2222222 sincossin2cos:2 kbabmma
(+)
22222222 cossincossin kbma 2222 kbma
Exercise 6C; 1, 3, 11, 15, 18a
Komaroni Unit 1