JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Consider ellipses \(E _{ k }: kx ^2+ k ^2 y ^2=1, k =1,2, \ldots\),\(20\). 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 \(\sum \limits_{ k =1}^{20} \frac{1}{ I _{ k }^2}\) is \(.......\).
- A \(3080\)
- B \(3210\)
- C \(3320\)
- D \(2870\)
Answer & Solution
Correct Answer
(A) \(3080\)
Step-by-step Solution
Detailed explanation
\(Kx x ^2+ K ^2 y ^2=1\) \(\frac{ x ^2}{1 / K }+\frac{ y ^2}{1 / K ^2}=1\) Now Equation of \(A _1 B _2 ; \frac{ x }{1 / \sqrt{ K }}+\frac{ y }{1 / K }=1 \Rightarrow \sqrt{ K } x + Ky =1\) \(r_K=\perp r\) distance of \((0,0)\) from line \(A_1 B_1\)…
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