JEE Main 2025 — Ellipse Question with Solution
JEE Main 2025 (4 Apr Shift 1)
Question
Let C be the circle and be two ellipses whose centres lie at the origin and major axes lie on x -axis and y -axis respectively. Let the straight line touch the curves , and at and respectively. Given that is the mid-point of the line segment and , the value of is equal to ______ .
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Show full solutionCorrect answer: 46
Correct answer
46
Step-by-step explanation
Let
Equation of tangent at
comparing with we get
Now parametric equation of
On solving we get
So,
$\begin{aligned}
& 9\left(2+\frac{5}{3} \times \frac{4}{3}+\frac{1}{3} \times \frac{8}{3}\right) \\ & \Rightarrow 46
\end{aligned}$
Equation of tangent at
comparing with we get
Now parametric equation of
On solving we get
So,
$\begin{aligned}
& 9\left(2+\frac{5}{3} \times \frac{4}{3}+\frac{1}{3} \times \frac{8}{3}\right) \\ & \Rightarrow 46
\end{aligned}$
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This is a previous-year question from JEE Main 2025, covering the Ellipse chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.