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The tangent at a point P(acosvarphi,bsin...

The tangent at a point `P(acosvarphi,bsinvarphi)` of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` meets its auxiliary circle at two points, the chord joining which subtends a right angle at the center. Find the eccentricity of the ellipse.

A

`(1+cos^2 theta)^(-1/2)`

B

`1+sin^2 theta`

C

`(1+sin^2 theta)^(-1/2)`

D

`1+cos^2 theta`

Text Solution

Verified by Experts

The correct Answer is:
C
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