JEE Main 2025MathematicsEllipseHardNumerical

JEE Main 2025Ellipse 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,
$\begin{aligned}
& 9\left(2+\frac{5}{3} \times \frac{4}{3}+\frac{1}{3} \times \frac{8}{3}\right) \\ & \Rightarrow 46
\end{aligned}$

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About this question

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.