If 5x + 9 = 0 is the directrix of the hyperbola 16x^2 – 9y^2 = 144, then its corresponding focus is :

$$\left( {{5 \over 3},0} \right)$$

$$\left( { - {5 \over 3},0} \right)$$

Hyperbola — JEE Main Previous Year Questions

67 solved PYQs · 2016–2026 · Mathematics

Solved PYQs: 67
Years covered: 2016–2026
Avg / year: ~6
Subject: Mathematics

How many JEE Main questions come from Hyperbola?

Hyperbola has contributed 67 questions to Joint Entrance Examination (Main) papers between 2016 and 2026 — an average of about 6 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 67 questions carries a written, step-by-step solution, and each is tagged to Hyperbola 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 Hyperbola questions from real JEE Main papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 67 Hyperbola questions (with full written solutions) are available in practice.

Question 1 · JEE Main 2021
The locus of the mid points of the chords of the hyperbola x^2 - y^2 = 4, which touch the parabola y^2 = 8x, is :
1. (A) $y^3 (x - 2) = x^2$
2. (B) $x^3 (x - 2) = y^2$
3. (C) $y^2 (x - 2) = x^3$
4. (D) $x^2 (x - 2) = y^3$
Show answerAnswer
$Answer: (C) y^2 (x - 2) = x^3$
Question 2 · JEE Main 2019
If 5x + 9 = 0 is the directrix of the hyperbola 16x^2 – 9y^2 = 144, then its corresponding focus is :
1. (A) $(\frac{5}{3}, 0)$
2. (B) $(5, 0)$
3. (C) $(- 5, 0)$
4. (D) $(- \frac{5}{3}, 0)$
Show answerAnswer
$Answer: (C) (- 5, 0)$
Question 3 · JEE Main 2019
If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is :
1. (A) $\frac{13}{6}$
2. (B) $2$
3. (C) $\frac{13}{12}$
4. (D) $\frac{13}{8}$
Show answerAnswer
$Answer: (C) \frac{13}{12}$
Question 4 · JEE Main 2019
A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis, distant 2b from the origin. Then the locus of the centre of this circle, is :
1. (A) $an ellipse$
2. (B) $a parabola$
3. (C) $a hyperbola$
4. (D) $a straight line$
Show answerAnswer
$Answer: (B) a parabola$
Question 5 · JEE Main 2019
A hyperbola has its centre at the origin, passes through the point (4, 2) and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is :
1. (A) $\frac{3}{2}$
2. (B) $3$
3. (C) $2$
4. (D) $\frac{2}{3}$
Show answerAnswer
$Answer: (D) \frac{2}{3}$

Hyperbola questions by year

Year	Questions	Share of chapter questions
2026	13
2025	9
2024	11
2023	5
2022	7
2021	5
2020	4
2019	7
2018	2
2017	1
2016	3

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FAQs

How many JEE Main questions have been asked from Hyperbola?

EByAi's bank holds 67 real JEE Main questions from Hyperbola, asked between 2016 and 2026 — about 6 per year on average. Every count is measured from actual papers, not estimated.

Is Hyperbola important for JEE Main?

67 questions over 11 papers make Hyperbola a steady-weightage chapter in JEE Main Mathematics. The year-wise table above shows exactly how often it appears.

Can I solve Hyperbola 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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