Consider ellipse E_k: k x² + k² y² = 1, for k = 1, 2, …, 20. Let… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 11 April, Shift 1Conic Sections (Parabola, Ellipse, Hyperbola)

Consider ellipse $E_k : k x^2 + k^2 y^2 = 1$ , for $k = 1, 2, \dots, 20$ . Let $C_k$ be the circle which touches the four chords joining the end points (one on the minor axis and another on the major axis) of the ellipse $E_k$ . If $r_k$ is the radius of the circle $C_k$ , then the value of $\sum_{k=1}^{20} \frac{1}{r_k^2}$ is:

A
$3320$
B
$3210$
C
$3080$
D
$2870$

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