JEE Main 2024 — Ellipse Question with Solution
JEE Main 2024 (05 Apr Shift 1)
Question
Let the line , intersect the -axis and -axis at the points and , respectively. If the equation of the circle having the line segment as a diameter is and the length of the latus rectum of the ellipse is , where and are coprime, then is equal to
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Show full solutionCorrect option: A
Correct answer
A11
Step-by-step explanation
Centre of the circle
Equation of diameter
$\begin{aligned}
& 2\left(\frac{3}{2}\right)+3(1)-\mathrm{k}=0 \\
& \Rightarrow \mathrm{k}=6
\end{aligned}$
Now, Equation of ellipse becomes
$\begin{aligned}
& x^2+9 y^2=36 \\
& \frac{x^2}{6^2}+\frac{y^2}{2^2}=1
\end{aligned}$
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This is a previous-year question from JEE Main 2024, 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.