JEE Main 2024 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 6 April 2024, Shift 1, Maths Q27

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

Let a conic

C

pass through the point

(4,-2)

and

P(x,y)

x \geq 3

, be any point on

C

. Let the slope of the line touching the conic

C

only at a single point

P

be half the slope of the line joining the points

P

and

(3,-5)

. If the focal distance of the point

(7,1)

C

d

, then

12d

equals __________.

Official answer

NTA final key.

Chapter: Conic Sections
Topic: General Conic Section
Idea tested: Condition for a Parabola

Same topic in other shifts

All General Conic Section questions

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
5 Apr 2026, Shift 1 · Q10Let P be a moving point on the circle $x^2 + y^2 - 6x - 8y + 21 = 0$ . Then, the maximum distance of P from the vertex of the parabola…MediumSingle 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 2025, Shift 2 · Q10Let for two distinct values of p the lines $y=x+p$ touch the ellipse $E:\frac{x^2}{4^2}+\frac{y^2}{3^2}=1$ at the points A and B. Let the…HardSingle correct
7 Apr 2025, Shift 1 · Q10Let P be the parabola, whose focus is $(-2, 1)$ and directrix is $2x + y + 2 = 0$ . Then the sum of the ordinates of the points on P, whose…MediumSingle 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.