Question

Consider ellipses E_k : kx² + k²y² = 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 rk is the radius of the circle C_k, then the value of \(\displaystyle\sum_{k=1}^{20}\frac{1}{r^2_k}\) is

(1) 3080 

(2) 3210 

(3) 3320 

(4) 2870

Answer 1

Correct option is (1) 3080

Now

Equation of

r_k = ⟂ r distance of (0,0) from line A₁B₁