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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) alpha`

B

`(1)/(sqrt(1 +sin^(2) alpha))`

C

`(1)/(sqrt( 1+ cos^(2) alpha ))`

D

`1 + sin^(2) alpha`

Text Solution

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The correct Answer is:
B
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