JEE Main 2024 — Parabola Question with Solution
JEE Main 2024 (09 Apr Shift 2)
Question
Consider the circle and the parabola . If the set of all values of , for which three chords of the circle on three distinct lines passing through the point are bisected by the parabola is the interval , then is equal to ________
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Show full solutionCorrect answer: 80
Correct answer
80
Step-by-step explanation
$\begin{aligned} & T=S_1 \\ & x_1+y_1=x_1^2+y_1^2 \\ & \alpha x_1=x_1^2+y_1^2 \\ & \alpha\left(2 t^2\right)=4 t^4+16 t^2 \\ & \alpha=2 t^2+8 \\ & \frac{\alpha-8}{2}=t^2 \end{aligned}4 \mathrm{t}^4+16 \mathrm{t}^2-4 < 0$ $\begin{aligned} & \mathrm{t}^2=-2+\sqrt{5} \\ & \alpha=4+2 \sqrt{5} \\ & \therefore \alpha \in(8,4+2 \sqrt{5}) \\ & \therefore(2 \mathrm{q}-\mathrm{p})^2=80 \end{aligned}$
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This is a previous-year question from JEE Main 2024, covering the Parabola 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.