JEE Main Maths · Conic Sections

Parabola Focal Chords in JEE Main

Name: Parabola Focal Chords: JEE Main previous year questions
Creator: Lumi

Parabola Focal Chords (Maths, Conic Sections) came 5 times in 5 of the 42 JEE Main shifts Lumi analysed, across 4 distinct ideas. 3 of them came in 2024–26; it was last asked in 2026.

Questions: 5; in 5 shifts
Ideas asked: 4; 1 asked more than once
Numerical answer: 0; 0% of its questions
Pattern: Frequent; last asked 2026

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 0Medium 4Hard 1

Format

Single correct5 Q

Ideas inside the topic

4 ideas

Parameter relation t1*t2 = -12 Q
Equation of focal chord1 Q
Ratio of Y-Coordinates of Extremities1 Q
Point of Contact of Focal Radius Circle with Vertex Tangent1 Q

Where it sits

Part of Conic Sections, which had 116 questions in all. Parabola Focal Chords accounts for 4% of them. In Lumi's JEE taxonomy it belongs to Coordinate Geometry.

Every question

All 5 Parabola Focal Chords questions

Newest first, each with its options and official answer.

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
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
9 Jan 2020, Shift 2 · Q66If one end of a focal chord AB of the parabola $y^2=8x$ is at $A\left(\frac{1}{2},-2\right)$ , then the equation of the tangent to it at B…MediumSingle correct