JEE Main 2021MathematicsHyperbolaHardNumerical

JEE Main 2021 — Hyperbola Question with Solution

JEE Main 2021 (25 Feb Shift 1)

Question

The locus of the point of intersection of the lines 3kx+ky-43=0 and 3x-y-43k=0 is a conic, whose eccentricity is

Enter your answer

Show full solutionCorrect answer: 2
Correct answer
2

Step-by-step explanation

The point of intersection of the lines 3kx+ky-43=0 and 3x-y-43k=0.

k=433x+y=3x-y43

⇒ 3x2-y2=48

⇒ x216-y248=1

Which is a hyperbola.

b2=a2e2-1

Now, 48=16e2-1

⇒ e=4=2

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.