JEE Main 2024 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 4 April 2024, Shift 2, Maths Q15

Question 15 of 90 in this shift, Maths question 15 of 30, Section A.

Let 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 passing through the points P and Q?

(1) $(3,-3)$
(2) $(2,-9)$
(3) $\left(\frac{3}{2},-16\right)$
(4) $\left(\frac{1}{2},-20\right)$ Official answer

Official answer

Option 4

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
9 Apr 2024, Shift 2 · Q27Consider 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…HardNumerical value
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.