Consider ellipses E_k: kx^2+k^2y^2=1, k = 1, 2,…,20. Let C_k be the circle which touches the four chords...

Question

Consider ellipses E_k: kx^2+k^2y^2=1, k = 1, 2,…,20. Let C_k be the circle which touches the four chords joining the end points (one on minor axis and another on major axis) of the ellipse E_k. If r_k is the radius of the circle C_k, then the value of _ k=1 ^ 20 1 r_k^2 is :

Accepted Answer

(A)

JEE Main 2023 Mathematics question

Solution