JEE Main 2020MathematicsHyperbolaMediumMCQ

JEE Main 2020 — Hyperbola Question with Solution

JEE Main 2020 (02 Sep Shift 1)

Question

A line parallel to the straight line 2x-y=0 is tangent to the hyperbola x24−y22=1 at the point x1, y1. Then x12+5y12 is equal to

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Show full solutionCorrect option: A
Correct answer
A6

Step-by-step explanation

Tangent at x1,y1

xx1-2yy1-4=0

This is parallel to 2x-y=0

⇒  x12y1=2

⇒  x1=4y1  ...1
Point x1,y1 lie on hyperbola x124-y122-1=0  ...2

Using equation 1 and 2, 4y12-y122=1⇒y12=27 & x12=327

We get x12+5y12=6

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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.