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Ellipse question

2023 · 11 Apr · Shift 1 · Q35

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PYQ Library
JEE Main
Mathematics
Ellipse
2023 · 11 Apr · Shift 1 · Q35

Ellipse question

2023 · 11 Apr · Shift 1 · Q35

JEE MainMathematicsEllipseMCQ+4 / −1

Consider ellipses

\mathrm{E}_{k}: k x^{2}+k^{2} y^{2}=1, k=1,2, \ldots, 20

. Let

\mathrm{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

\mathrm{E}_{k}

. If

r_{k}

is the radius of the circle

\mathrm{C}_{k}

, then the value of

\sum_{k=1}^{20} \frac{1}{r_{k}^{2}}

is :

A
2870
B
3210
C
3320
D
3080

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