JEE Main 2021MathematicsHyperbolaMediumMCQ

JEE Main 2021 — Hyperbola Question with Solution

JEE Main 2021 (25 Feb Shift 2)

Question

A hyperbola passes through the foci of the ellipse x225+y216=1 and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is:

Choose an option

Show full solutionCorrect option: A
Correct answer
Ax29-y216=1

Step-by-step explanation

For ellipse e1=1-b2a2=35

for hyperbola e2=53

Let hyperbola be

x2a2-y2b2=1

∵ it passes through 3,0⇒9a2=1

⇒a2=9

⇒b2=a2e2-1

=9259-1=16

∴ Hyperbola is

x29-y216=1

option 1

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Hyperbola chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2021, covering the Hyperbola chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.