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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)

Badiuddin askIITians.ismu Expert
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

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Badiuddin

7 years ago
Badiuddin askIITians.ismu Expert
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,


Askiitians Experts


 Badiuddin

7 years ago
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