JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 26 August 2021, Shift 2, Maths Q73

Question 73 of 90 in this shift, Maths question 13 of 30, Section A.

The locus of the mid points of the chords of the hyperbola

x^2-y^2=4

, which touch the parabola

y^2=8x

, is :

(1) $x^3(x-2)=y^2$
(2) $x^2(x-2)=y^3$
(3) $y^2(x-2)=x^3$ Official answer
(4) $y^3(x-2)=x^2$

Official answer

Option 3

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
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

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.