JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 6 April 2026, Shift 2, Maths Q12

Question 12 of 75 in this shift, Maths question 12 of 25, Section A.

Let

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

, be a focus of E and AB be a chord passing through P. Then the locus of the mid point of AB is :

(1) $9y^2=8x(1-x)$ Official answer
(2) $3y^2=4x(1-x)$
(3) $9y^2=8x(x-1)$
(4) $3y^2=4x(x-1)$

Official answer

Option 1

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 4× in all

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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 42 of the 174 JEE Main shifts held from 2017 to 2026.