A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to the curve C at the point P meets the x-axis at Q. If the y-axis bisects the segment PQ, then C is a parabola with :

focus $$\left( {{4 \over 3},0} \right)$$

focus $$\left( {0,{3 \over 4}} \right)$$

If the area of the triangle whose one vertex is at the vertex of the parabola, y^2 + 4(x – a^2 ) = 0 and the other two vertices are the points of intersection of the parabola and y-axis, is 250 sq. units, then a value of 'a' is :

$${\left( {10} \right)^{2/3}}$$

$$5\left( {{2^{1/3}}} \right)$$

Parabola — JEE Main Previous Year Questions

77 solved PYQs · 2018–2026 · Mathematics

Solved PYQs: 77
Years covered: 2018–2026
Avg / year: ~9
Subject: Mathematics

How many JEE Main questions come from Parabola?

Parabola has contributed 77 questions to Joint Entrance Examination (Main) papers between 2018 and 2026 — an average of about 9 questions a year. That count is measured from EByAi’s bank of 55,289 JEE Main questions, not estimated from a syllabus. Every one of the 77 questions carries a written, step-by-step solution, and each is tagged to Parabola within Mathematics, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample Parabola questions from real JEE Main papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 77 Parabola questions (with full written solutions) are available in practice.

Question 1 · JEE Main 2022
If vertex of a parabola is (2, -1) and the equation of its directrix is 4x - 3y = 21, then the length of its latus rectum is :
1. (A) $2$
2. (B) $8$
3. (C) $12$
4. (D) $16$
Show answerAnswer
$Answer: (B) 8$
Question 2 · JEE Main 2022
A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to the curve C at the point P meets the x-axis at Q. If the y-axis bisects the segment PQ, then C is a parabola with :
1. (A) $length of latus rectum 3$
2. (B) $length of latus rectum 6$
3. (C) $focus (\frac{4}{3}, 0)$
4. (D) $focus (0, \frac{3}{4})$
Show answerAnswer
$Answer: (A) length of latus rectum 3$
Question 3 · JEE Main 2021
If two tangents drawn from a point P to the parabola y^2 = 16(x - 3) are at right angles, then the locus of point P is :
1. (A) $x + 3 = 0$
2. (B) $x + 1 = 0$
3. (C) $x + 2 = 0$
4. (D) $x + 4 = 0$
Show answerAnswer
$Answer: (B) x + 1 = 0$
Question 4 · JEE Main 2019
If the area of the triangle whose one vertex is at the vertex of the parabola, y^2 + 4(x – a^2 ) = 0 and the other two vertices are the points of intersection of the parabola and y-axis, is 250 sq. units, then a value of 'a' is :
1. (A) $55$
2. (B) $(10)^{2/3}$
3. (C) $5 (2^{1/3})$
4. (D) $5$
Show answerAnswer
$Answer: (D) 5$
Question 5 · JEE Main 2018
Tangents drawn from the point (-8, 0) to the parabola y² = 8x touch the parabola at P and Q. If F is the focus of the parabola, then the area of the triangle PFQ (in sq. units) is equal to :
1. (A) $24$
2. (B) $32$
3. (C) $48$
4. (D) $64$
Show answerAnswer
$Answer: (C) 48$

Parabola questions by year

Year	Questions	Share of chapter questions
2026	14
2025	17
2024	12
2023	5
2022	9
2021	7
2020	4
2019	8
2018	1

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FAQs

How many JEE Main questions have been asked from Parabola?

EByAi's bank holds 77 real JEE Main questions from Parabola, asked between 2018 and 2026 — about 9 per year on average. Every count is measured from actual papers, not estimated.

Is Parabola important for JEE Main?

77 questions over 9 papers make Parabola a steady-weightage chapter in JEE Main Mathematics. The year-wise table above shows exactly how often it appears.

Can I solve Parabola PYQs online for free?

Yes. EByAi lets you solve JEE Main past-year questions in the browser with written solutions — free daily practice, no card needed.

More JEE Main Mathematics chapters

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