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

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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.