JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 29 June 2022, Shift 2, Maths Q10

Question 10 of 90 in this shift, Maths question 10 of 30, Section A.

Let P :

y^2 = 4ax

a > 0

be a parabola with focus S. Let the tangents to the parabola P make an angle of

\frac{\pi}{4}

with the line

y = 3x + 5

touch the parabola P at A and B. Then the value of

a

for which A, B and S are collinear is

(1)8 only
(2)2 only
(3) $\frac{1}{4}$ only
(4)any $a > 0$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Conic Sections
Topic: Parabola Focal Chords
Idea tested: Chord of Contact from Directrix is Focal

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
2 Apr 2025, Shift 2 · Q11Let 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…MediumSingle correct
4 Apr 2024, Shift 1 · Q28Let the length of the focal chord PQ of the parabola $y^2=12x$ be 15 units. If the distance of PQ from the origin is p, then $10p^2$ is…MediumNumerical value
5 Apr 2024, Shift 1 · Q28Suppose AB is a focal chord of the parabola $y^2=12x$ of length $l$ and slope $m<\sqrt3$ . If the distance of the chord AB from the origin…MediumNumerical value
8 Apr 2023, Shift 1 · Q14Let $R$ 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…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.