Tangents at A(a cos theta1, b sin theta1...

Tangents at `A(a cos theta_1, b sin theta_1)" and "B(a cos theta_2, b sin theta_2)` to the ellipse are `(x^2)/(a^2)+(y^2)/(b^2)=1` perpendicular and their point of intersection is `T(x_1,y_1)`. Normal at A and B meet at point N(h, k). Then:

A

`(a^2+b^2)cos^2((theta_1- theta_2)/(2))=a^2 cos^2((theta_1+theta_2)/(2))+b^2 sin^2((theta_1+theta_2)/(2))`

B

Origin, N and T are vertices of a right-angle triangle

C

`cos^2 ((theta_1-theta_2)/(2))=(a^2+b^2)/((a+b)^2)`

D

Origin, N and T are collinear points

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The correct Answer is:

D

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