JEE Main 2020MathematicsHyperbolaMediumMCQ

JEE Main 2020 — Hyperbola Question with Solution

JEE Main 2020 (03 Sep Shift 1)

Question

A hyperbola having the transverse axis of length, 2 has the same foci as that of the ellipse, 3x2+4y2=12 then this hyperbola does not pass through which of the following points?

Choose an option

Show full solutionCorrect option: D
Correct answer
D32,12

Step-by-step explanation

Equation of ellipse : x24+y23=1

⇒e=1-34=12

Foci of the ellipse: ±2×12,0 i.e.,±1,0

For hyperbola: Length of the transverse axis=2a=2⇒a=12

Foci of hyperbola ±1,0⇒ae=1

b2=a2e2-a2=1-12=12

Equation of hyperbola :x21/2-x21/2=1

⇒x2-y2=12⇒2x2-2y2=1

Only the point, 32,12 does not satisfy the above equation.

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About this question

This is a previous-year question from JEE Main 2020, 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.