Hyperbola5 questions5 PYQ

Hyperbola — JEE Maths Practice Questions & Solutions

5 questions on Hyperbola with full step-by-step solutions, including past-year (PYQ) problems. Free to practice.

hardPYQ · JEE Main 2026

e_1

and

e_2

be two distinct roots of the equation

x^2-ax+2=0

. Let the set

\{a\in\mathbb{R}:e_1,e_2

are eccentricities of hyperbolas

\}=(\alpha,\beta)

and

\{a\in\mathbb{R}:e_1,e_2

are the eccentricities of an ellipse and a hyperbola respectively

\}=(\gamma,\infty)

. Then

\alpha^2+\beta^2+\gamma^2

is equal to

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mediumPYQ · JEE Main 2026

If the eccentricity

e

of the hyperbola

\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1

, passing through

\left(6,4\sqrt3\right)

, satisfies

15(e^2+1)=34e

, then the length of the latus rectum of the hyperbola

\dfrac{x^2}{b^2}-\dfrac{y^2}{2(a^2+1)}=1

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mediumPYQ · JEE Main 2026

Let

O

be the origin, and

P

and

Q

be two points on the rectangular hyperbola

xy=12

such that the mid point of the line segment

PQ

\left(\dfrac12,-\dfrac12\right)

. Then the area of the triangle

OPQ

equals

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mediumPYQ · JEE Main 2026

Let

H:\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1

be a hyperbola such that the distance between its foci is

6

and the distance between its directrices is

\dfrac83

. If the line

x=\alpha

intersects

H

A

and

B

such that the area of

\triangle AOB

4\sqrt{15}

, where

O

is the origin, then

\alpha^2

equals

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mediumPYQ · JEE Main 2026

Let the eccentricity

e

of a hyperbola satisfy

6e^2-11e+3=0

. If the foci are

(3,5)

and

(3,-4)

, then the length of its latus rectum is:

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