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Vaibhav Mathur Grade: 12
```        If (x/a)2 +(y/b)2=1(a>b) and x2 -y2 =c2 cut at right angles, then
a. a2+b2=2c2
b. b2-a2=2c2
c.a2 -b2=2c2
d. a2 -b2=2c2```
7 years ago

## Answers : (2)

147 Points
```										Dear Vaibhav

let a point on ellipse is (acosT ,bsinT)(let this is point where curve intersect each other)
so normal at this point on ellipse,and tangent on hyperbola will be same line.
normal on ellipse
axsecT - by cosecT =a^2 -b^2 ..............1

tangent on parabola at (acosT ,bsinT)

axcosT - by sinT =c^2 .....................2

equation 1 and 2 represent the same equation
so

asecT /acosT  = bcosecT /b sinT   = (a^2 -b^2) /c^2

so
asecT /acosT  = bcosecT /b sinT
cos^2T  = sin^2T
or   tanT =1
or   T =45

and  bcosecT /b sinT   = (a^2 -b^2) /c^2

a2 -b2=2c^2

Please feel free to post as many doubts on our discussion forum as you can.
If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly.
We are all IITians and here to help you in your IIT JEE  & AIEEE preparation.

All the best.

Regards,

```
7 years ago
147 Points
```										Dear Vaibhav l
et a point on ellipse is (acosΘ ,bsinΘ)(let this is point where curve intersect each other)
so normal at this point on ellipse,and tangent on hyperbola will be same line.
normal on ellipse axsecΘ - by cosecΘ =a^2 -b^2 ..............1
tangent on parabola at (acosΘ ,bsinΘ) is  axcosΘ - by sinΘ =c^2 .....................2
equation 1 and 2 represent the same equation
so asecΘ /acosΘ= bcosecΘ /b sinΘ = (a^2 -b^2) /c^2
so asecΘ /acosΘ= bcosecΘ /b sinΘ
cos^2Θ= sin^2Θ
or tanΘ =1
or Θ =45
and bcosecΘ /b sinΘ = (a^2 -b^2) /c^2
a2 -b2=2c^2
Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE & AIEEE preparation.
All the best. Regards,
```
7 years ago
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