JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 24 February 2021, Shift 1, Maths Q74

Question 74 of 90 in this shift, Maths question 14 of 30, Section A.

The locus of the mid-point of the line segment joining the focus of the parabola

y^2 = 4ax

to a moving point of the parabola, is another parabola whose directrix is :

(1) $x = a$
(2) $x = -\frac{a}{2}$
(3) $x = 0$ Official answer
(4) $x = \frac{a}{2}$

Official answer

Option 3

NTA final key.

Chapter: Conic Sections
Topic: General Conic Section
Idea tested: Focus-Directrix Form Extraction

Same idea in other shifts

Asked 4× in all

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
25 Jun 2022, Shift 1 · Q19Let $x=2t$ , $y=\frac{t^2}{3}$ be a conic. Let S be the focus and B be the point on the axis of the conic such that $SA\perp BA$ , where A…HardSingle correct
27 Jun 2022, Shift 2 · Q11If the equation of the parabola, whose vertex is at $(5, 4)$ and the directrix is $3x+y-29=0$ , is $x^2+ay^2+bxy+cx+dy+k=0$ , then…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.