x2 t03 05 rectangular hyperbola (2011)
TRANSCRIPT
![Page 1: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/1.jpg)
Rectangular Hyperbola
![Page 2: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/2.jpg)
Rectangular HyperbolaA hyperbola whose asymptotes are perpendicular to each other
![Page 3: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/3.jpg)
Rectangular HyperbolaA hyperbola whose asymptotes are perpendicular to each other
1
ab
ab
![Page 4: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/4.jpg)
Rectangular HyperbolaA hyperbola whose asymptotes are perpendicular to each other
1
ab
ab
abab
22
![Page 5: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/5.jpg)
Rectangular HyperbolaA hyperbola whose asymptotes are perpendicular to each other
1
ab
ab
abab
22
equation;thehas hyperbola
222
2
2
2
2
1
ayxay
ax
![Page 6: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/6.jpg)
Rectangular HyperbolaA hyperbola whose asymptotes are perpendicular to each other
1
ab
ab
abab
22
222 1 aea equation;thehas hyperbola
222
2
2
2
2
1
ayxay
ax
![Page 7: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/7.jpg)
Rectangular HyperbolaA hyperbola whose asymptotes are perpendicular to each other
1
ab
ab
abab
22
222 1 aea equation;thehas hyperbola
222
2
2
2
2
1
ayxay
ax
2211
2
2
ee
e
![Page 8: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/8.jpg)
Rectangular HyperbolaA hyperbola whose asymptotes are perpendicular to each other
1
ab
ab
abab
22
222 1 aea equation;thehas hyperbola
222
2
2
2
2
1
ayxay
ax
2211
2
2
ee
e
2 isty eccentrici
![Page 9: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/9.jpg)
y
x
Y
X
yxP ,
![Page 10: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/10.jpg)
y
x
Y
X
yxP ,In order to make the asymptotes the coordinate axes we need to rotate the curve 45 degrees anticlockwise.
![Page 11: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/11.jpg)
y
x
Y
X
yxP ,In order to make the asymptotes the coordinate axes we need to rotate the curve 45 degrees anticlockwise.
45cisby multiplied is , i.e. iyxyxP
![Page 12: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/12.jpg)
y
x
Y
X
yxP ,In order to make the asymptotes the coordinate axes we need to rotate the curve 45 degrees anticlockwise.
45cisby multiplied is , i.e. iyxyxP 45sin45cos iiyx
21
21 iiyx
![Page 13: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/13.jpg)
y
x
Y
X
yxP ,In order to make the asymptotes the coordinate axes we need to rotate the curve 45 degrees anticlockwise.
45cisby multiplied is , i.e. iyxyxP 45sin45cos iiyx
21
21 iiyx
iyxyx
yiyixx
iiyx
22
21
12
1
![Page 14: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/14.jpg)
y
x
Y
X
yxP ,In order to make the asymptotes the coordinate axes we need to rotate the curve 45 degrees anticlockwise.
45cisby multiplied is , i.e. iyxyxP 45sin45cos iiyx
21
21 iiyx
iyxyx
yiyixx
iiyx
22
21
12
1
2
2yxYyxX
![Page 15: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/15.jpg)
y
x
Y
X
yxP ,In order to make the asymptotes the coordinate axes we need to rotate the curve 45 degrees anticlockwise.
45cisby multiplied is , i.e. iyxyxP 45sin45cos iiyx
21
21 iiyx
iyxyx
yiyixx
iiyx
22
21
12
1
2
2yxYyxX
2
22 yxXY
![Page 16: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/16.jpg)
y
x
Y
X
yxP ,In order to make the asymptotes the coordinate axes we need to rotate the curve 45 degrees anticlockwise.
45cisby multiplied is , i.e. iyxyxP 45sin45cos iiyx
21
21 iiyx
iyxyx
yiyixx
iiyx
22
21
12
1
2
2yxYyxX
2
22 yxXY
2
2aXY
![Page 17: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/17.jpg)
focus; 0,ae
0,2a
![Page 18: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/18.jpg)
focus; 0,ae
0,2a
aia
ia
21
212
![Page 19: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/19.jpg)
focus; 0,ae
0,2a
aia
ia
21
212
aa,focus
![Page 20: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/20.jpg)
focus; 0,ae
0,2a
aia
ia
21
212
aa,focus
directrix;eax
2ax
![Page 21: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/21.jpg)
focus; 0,ae
0,2a
aia
ia
21
212
aa,focus
directrix;eax
2ax
xyy
to|| rotatedwhen axisto||aresdirectrice
![Page 22: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/22.jpg)
focus; 0,ae
0,2a
aia
ia
21
212
aa,focus
directrix;eax
2ax
xyy
to|| rotatedwhen axisto||aresdirectrice
0formin thus kyx
![Page 23: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/23.jpg)
focus; 0,ae
0,2a
aia
ia
21
212
aa,focus
directrix;eax
2ax
xyy
to|| rotatedwhen axisto||aresdirectrice
0formin thus kyx
22 is sdirectricebetween distance Now a
![Page 24: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/24.jpg)
focus; 0,ae
0,2a
aia
ia
21
212
aa,focus
directrix;eax
2ax
xyy
to|| rotatedwhen axisto||aresdirectrice
0formin thus kyx
22 is sdirectricebetween distance Now a
2 isdirectrix origin to from distance a
![Page 25: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/25.jpg)
focus; 0,ae
0,2a
aia
ia
21
212
aa,focus
directrix;eax
2ax
xyy
to|| rotatedwhen axisto||aresdirectrice
0formin thus kyx
22 is sdirectricebetween distance Now a
2 isdirectrix origin to from distance a
2200 ak
![Page 26: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/26.jpg)
focus; 0,ae
0,2a
aia
ia
21
212
aa,focus
directrix;eax
2ax
xyy
to|| rotatedwhen axisto||aresdirectrice
0formin thus kyx
22 is sdirectricebetween distance Now a
2 isdirectrix origin to from distance a
2200 ak
akak
![Page 27: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/27.jpg)
focus; 0,ae
0,2a
aia
ia
21
212
aa,focus
directrix;eax
2ax
xyy
to|| rotatedwhen axisto||aresdirectrice
0formin thus kyx
22 is sdirectricebetween distance Now a
2 isdirectrix origin to from distance a
2200 ak
akak
ayx aresdirectrice
![Page 28: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/28.jpg)
The rectangular hyperbola with x and y axes as aymptotes, has the equation;
2
21 axy
where; aa , :foci
ayx :sdirectrice
2ty eccentrici
![Page 29: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/29.jpg)
The rectangular hyperbola with x and y axes as aymptotes, has the equation;
2
21 axy
where; aa , :foci
ayx :sdirectrice
2ty eccentrici
2 cxyofsCoordinateParametric
![Page 30: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/30.jpg)
The rectangular hyperbola with x and y axes as aymptotes, has the equation;
2
21 axy
where; aa , :foci
ayx :sdirectrice
2ty eccentrici
2 cxyofsCoordinateParametric
ctx tcy
![Page 31: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/31.jpg)
The rectangular hyperbola with x and y axes as aymptotes, has the equation;
2
21 axy
where; aa , :foci
ayx :sdirectrice
2ty eccentrici
2 cxyofsCoordinateParametric
ctx tcy
Tangent: ctytx 22
![Page 32: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/32.jpg)
The rectangular hyperbola with x and y axes as aymptotes, has the equation;
2
21 axy
where; aa , :foci
ayx :sdirectrice
2ty eccentrici
2 cxyofsCoordinateParametric
ctx tcy
Tangent: ctytx 22 Normal: 143 tctyxt
![Page 33: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/33.jpg)
e.g. (i) (1991)The hyperbola H is xy= 4
a) Sketch H showing where H intersects the axis of symmetry.
![Page 34: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/34.jpg)
e.g. (i) (1991)The hyperbola H is xy= 4
a) Sketch H showing where H intersects the axis of symmetry.y
x
y = x
![Page 35: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/35.jpg)
e.g. (i) (1991)The hyperbola H is xy= 4
a) Sketch H showing where H intersects the axis of symmetry.y
x
y = x
244
2
xxxy
2,2
2,2
![Page 36: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/36.jpg)
e.g. (i) (1991)The hyperbola H is xy= 4
a) Sketch H showing where H intersects the axis of symmetry.y
x
y = x
244
2
xxxy
2,2
2,2
tytxt
tP 4 is 2,2at tangent that theShow b) 2
![Page 37: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/37.jpg)
e.g. (i) (1991)The hyperbola H is xy= 4
a) Sketch H showing where H intersects the axis of symmetry.y
x
y = x
244
2
xxxy
2,2
2,2
tytxt
tP 4 is 2,2at tangent that theShow b) 2
24
4
xdxdy
xy
![Page 38: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/38.jpg)
e.g. (i) (1991)The hyperbola H is xy= 4
a) Sketch H showing where H intersects the axis of symmetry.y
x
y = x
244
2
xxxy
2,2
2,2
tytxt
tP 4 is 2,2at tangent that theShow b) 2
24
4
xdxdy
xy
2
2
1
24,2when
t
tdxdytx
![Page 39: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/39.jpg)
e.g. (i) (1991)The hyperbola H is xy= 4
a) Sketch H showing where H intersects the axis of symmetry.y
x
y = x
244
2
xxxy
2,2
2,2
tytxt
tP 4 is 2,2at tangent that theShow b) 2
24
4
xdxdy
xy
2
2
1
24,2when
t
tdxdytx
txtt
y 2122
![Page 40: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/40.jpg)
e.g. (i) (1991)The hyperbola H is xy= 4
a) Sketch H showing where H intersects the axis of symmetry.y
x
y = x
244
2
xxxy
2,2
2,2
tytxt
tP 4 is 2,2at tangent that theShow b) 2
24
4
xdxdy
xy
2
2
1
24,2when
t
tdxdytx
txtt
y 2122
tytxtxtyt
422
2
2
![Page 41: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/41.jpg)
tstsstM
ssQPtss
4,4at intersect
2,2 and at tangents that theshow ,,0 c) 22
![Page 42: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/42.jpg)
tstsstM
ssQPtss
4,4at intersect
2,2 and at tangents that theshow ,,0 c) 22
tytxP 4: 2 sysxQ 4: 2
![Page 43: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/43.jpg)
tstsstM
ssQPtss
4,4at intersect
2,2 and at tangents that theshow ,,0 c) 22
tytxP 4: 2 sysxQ 4: 2
styst 4422
![Page 44: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/44.jpg)
tstsstM
ssQPtss
4,4at intersect
2,2 and at tangents that theshow ,,0 c) 22
tytxP 4: 2 sysxQ 4: 2
styst 4422
tsy
stystst
4
4
![Page 45: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/45.jpg)
tstsstM
ssQPtss
4,4at intersect
2,2 and at tangents that theshow ,,0 c) 22
tytxP 4: 2 sysxQ 4: 2
styst 4422
tsy
stystst
4
4
tts
tx 44 2
![Page 46: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/46.jpg)
tstsstM
ssQPtss
4,4at intersect
2,2 and at tangents that theshow ,,0 c) 22
tytxP 4: 2 sysxQ 4: 2
styst 4422
tsy
stystst
4
4
tts
tx 44 2
tsst
tsttstx
4
444 22
![Page 47: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/47.jpg)
tstsstM
ssQPtss
4,4at intersect
2,2 and at tangents that theshow ,,0 c) 22
tytxP 4: 2 sysxQ 4: 2
styst 4422
tsy
stystst
4
4
tts
tx 44 2
tsst
tsttstx
4
444 22
tstsstM 4,4 is
![Page 48: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/48.jpg)
origin. theincludingnot but origin, he through tline
straight a is of locus that theshow,1 that Suppose d) Mt
s
![Page 49: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/49.jpg)
origin. theincludingnot but origin, he through tline
straight a is of locus that theshow,1 that Suppose d) Mt
s
tsy
tsstx
4 4
![Page 50: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/50.jpg)
origin. theincludingnot but origin, he through tline
straight a is of locus that theshow,1 that Suppose d) Mt
s
tsy
tsstx
4 4
ts 1
1st
![Page 51: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/51.jpg)
origin. theincludingnot but origin, he through tline
straight a is of locus that theshow,1 that Suppose d) Mt
s
tsy
tsstx
4 4
ts 1
4xs t
1st
![Page 52: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/52.jpg)
origin. theincludingnot but origin, he through tline
straight a is of locus that theshow,1 that Suppose d) Mt
s
tsy
tsstx
4 4
ts 1
4xs t
4ys t
x
1st
![Page 53: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/53.jpg)
origin. theincludingnot but origin, he through tline
straight a is of locus that theshow,1 that Suppose d) Mt
s
tsy
tsstx
4 4
ts 1
4xs t
4ys t
x
xy
1st
![Page 54: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/54.jpg)
origin. theincludingnot but origin, he through tline
straight a is of locus that theshow,1 that Suppose d) Mt
s
tsy
tsstx
4 4
ts 1
4xs t
4ys t
x
xy 0,0 thus,04
M
ts
1st
![Page 55: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/55.jpg)
origin. theincludingnot but origin, he through tline
straight a is of locus that theshow,1 that Suppose d) Mt
s
tsy
tsstx
4 4
ts 1
4xs t
4ys t
x
xy 0,0 thus,04
M
ts 0,0excluding,isoflocus xyM
1st
![Page 56: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/56.jpg)
(ii) aSPPS 2 that Show
x
yxP ,
SS
![Page 57: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/57.jpg)
(ii) aSPPS 2 that Show
y
x
yxP ,
SS
By definition of an ellipse;
![Page 58: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/58.jpg)
(ii) aSPPS 2 that Show
y
x
yxP ,
SS
By definition of an ellipse;
ePMSPPS
eax
M
eax
![Page 59: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/59.jpg)
(ii) aSPPS 2 that Show
y
x
yxP ,
SS
By definition of an ellipse;
ePMSPPS MeP
eax
M
eax
M
![Page 60: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/60.jpg)
(ii) aSPPS 2 that Show
y
x
yxP ,
SS
By definition of an ellipse;
ePMSPPS MeP
eax
M
eax
M
MPPMe
aeae
2
2
![Page 61: X2 T03 05 rectangular hyperbola (2011)](https://reader034.vdocuments.us/reader034/viewer/2022052700/55a1e4ee1a28ab94508b46f0/html5/thumbnails/61.jpg)
(ii) aSPPS 2 that Show
y
x
yxP ,
SS
By definition of an ellipse;
ePMSPPS MeP
eax
M
eax
M
MPPMe
aeae
2
2
Exercise 6D; 3, 4, 7, 10, 11a,12, 14, 19, 21, 26, 29,
31, 43, 47