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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

`e^(2)(1+cos^(2)theta)=1`

B

`e^(2)(cosec^(2)theta+1)=1`

C

`e^(2)(1+sin^(2)theta)=1`

D

`e^(2)(1+tan^(2)theta)=1`

Text Solution

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The correct Answer is:
C
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