JEE Main 2020MathematicsHyperbolaMediumMCQ

JEE Main 2020 — Hyperbola Question with Solution

JEE Main 2020 (04 Sep Shift 1)

Question

Let P3,3 be a point on the hyperbola, x2a2-y2b2=1. If the normal to it at P intersects the x-axis at 9,0 and e is its eccentricity, then the ordered pair a2,e2 is equal to:

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Show full solutionCorrect option: A
Correct answer
A92,3

Step-by-step explanation

Given hyperbola is x2a2−y2b2=1.

P3,3 lies on hyperbola then 1a2−1b2=19  ...1

Normal at 3, 3 is a2x3+b2y3=a2+b2

Normal passes through 9, 0

3a2=a2+b2 ⇒2a2=b2

Then using (1), 1a2−12a2=19

2a2=9⇒a2=92 and b2=9

e2=1+b2a2=1+2=3.

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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.