JEE Main 2016MathematicsHyperbolaMediumMCQ

JEE Main 2016 — Hyperbola Question with Solution

JEE Main 2016 (10 Apr Online)

Question

A hyperbola whose transverse axis is along the major axis of the conic x23+y24=4 and has vertices at the foci of the conic. If the eccentricity of the hyperbola is 32, then which of the following points does not lie on the hyperbola ?

Choose an option

Show full solutionCorrect option: C
Correct answer
C5,23

Step-by-step explanation

Given conic is x212+y216=1

e= 1-1216=12

Foci 0,2 and 0,-2.

So, transverse axis of hyperbola=2b=4.

⇒b=2

Given e=32

And a2=b2e2-1

⇒a2=4 94-1

⇒a2=5

∴ The equation of hyperbola is x25-y24=-1.

Now, Check options.

Clearly, the point 5,23 does not satisfy above equation.

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About this question

This is a previous-year question from JEE Main 2016, 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.