Let the point $P$ of the focal chord $PQ$ of the parabola $y^2 = 16x$ be $(1, -4)$. If the focus of the parabola divides the chord $PQ$ in the ratio $m : n$, $\gcd(m, n) = 1$, then $m^2 + n^2$ is equal to :

JEE Main 2025 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 2 April 2025, Shift 2, Maths Q11

Question 11 of 75 in this shift, Maths question 11 of 25, Section A.

Let the point

P

of the focal chord

PQ

of the parabola

y^2 = 16x

(1, -4)

. If the focus of the parabola divides the chord

PQ

in the ratio

m : n

\gcd(m, n) = 1

, then

m^2 + n^2

is equal to :

(1) $10$
(2) $17$ Official answer
(3) $26$
(4) $37$

Official answer

Option 2

NTA final key.

Chapter: Conic Sections
Topic: Parabola Focal Chords
Idea tested: Ratio of Y-Coordinates of Extremities

Same topic in other shifts

All Parabola Focal Chords questions

5 Apr 2026, Shift 2 · Q12Let the directrix of the parabola $P: y^2=8x$ , cut x-axis at the point A. Let $B(\alpha, \beta)$ , $\alpha>1$ , be a point on P such that…MediumSingle correct
2 Apr 2025, Shift 1 · Q1Let the focal chord PQ of the parabola $y^2=4x$ make an angle of $60^\circ$ with the positive $x$ -axis, where P lies in the first…MediumSingle correct
29 Jun 2022, Shift 1 · Q18Let PQ be a focal chord of the parabola $y^2 = 4x$ such that it subtends an angle of $\frac{\pi}{2}$ at the point $(3, 0)$ . Let the line…HardSingle correct
9 Jan 2020, Shift 2 · Q66If one end of a focal chord AB of the parabola $y^2=8x$ is at $A\left(\frac{1}{2},-2\right)$ , then the equation of the tangent to it at B…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 42 of the 174 JEE Main shifts held from 2017 to 2026.