JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 8 April 2023, Shift 1, Maths Q14

Question 14 of 90 in this shift, Maths question 14 of 30, Section A.

Let

R

be the focus of the parabola

y^2=20x

and the line

y=mx+c

intersect the parabola at two points

P

and

Q

. Let the point

G(10,10)

be the centroid of the triangle

PQR

. If

c-m=6

, then

(PQ)^2

(1) $296$
(2) $325$ Official answer
(3) $317$
(4) $346$

Official answer

Option 2

NTA final key.

Chapter: Conic Sections
Topic: Parabola Focal Chords
Idea tested: Equation of focal chord

Same idea in other shifts

Asked 3× in all

29 Jul 2022, Shift 1 · Q17Let the focal chord of the parabola $P : y^2 = 4x$ along the line $L : y = mx + c$ , $m > 0$ meet the parabola at the points M and N. Let…HardSingle 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

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.