JEE Main 2024 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 9 April 2024, Shift 2, Maths Q27

Question 27 of 90 in this shift, Maths question 27 of 30, Section B.

Consider the circle

C: x^2+y^2=4

and the parabola

P: y^2=8x

. If the set of all values of

\alpha

, for which three chords of the circle

C

on three distinct lines passing through the point

(\alpha, 0)

are bisected by the parabola

P

is the interval

(p, q)

, then

(2q-p)^2

is equal to __________.

Official answer

NTA final key.

Chapter: Conic Sections
Topic: General Conic Section
Idea tested: Chord Bisected at a Given Point (T=S1)

Same idea in other shifts

Asked 7× in all

2 Apr 2026, Shift 2 · Q11Let $O$ be the origin, and $P$ and $Q$ be two points on the rectangular hyperbola $xy = 12$ such that the midpoint of the line segment…MediumSingle correct
4 Apr 2026, Shift 1 · Q13Suppose that two chords, drawn from the point $(1,2)$ on the circle $x^2+y^2+x-3y=0$ are bisected by the $y$ -axis. If the other ends of…HardSingle correct
6 Apr 2026, Shift 2 · Q12Let $x=9$ be a directrix of an ellipse E, whose centre is at the origin and eccentricity is $\frac{1}{3}$ . Let P $(\alpha,0)$ , $\alpha>0$ ,…MediumSingle correct
4 Apr 2024, Shift 2 · Q15Let PQ be a chord of the parabola $y^2=12x$ and the midpoint of PQ be at $(4,1)$ . Then, which of the following point lies on the line…MediumSingle correct
27 Jan 2024, Shift 1 · Q16The length of the chord of the ellipse $\dfrac{x^2}{25}+\dfrac{y^2}{16}=1$ , whose mid point is $\left(1, \dfrac{2}{5}\right)$ , is equal to :HardSingle correct
26 Aug 2021, Shift 2 · Q73The locus of the mid points of the chords of the hyperbola $x^2-y^2=4$ , which touch the parabola $y^2=8x$ , is :HardSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.