JEE Main 2018MathematicsStraight LinesMediumMCQ

JEE Main 2018 — Straight Lines Question with Solution

JEE Main 2018 (16 Apr Online)

Question

The locus of the point of intersection of the lines 2x-y+42k=0 and 2kx+ky-42=0 (k is any non-zero real parameter) is

Choose an option

Show full solutionCorrect option: C
Correct answer
Ca hyperbola with length of its transverse axis 82

Step-by-step explanation

Given equation of lines are 2x-y+42k=0     ...1

and 2kx+ky-42=0      ...2 

Eliminating k from 1 and 2,

⇒2x+y2x-y-42=42

⇒2x2-y2=-32

⇒y232-x216=1, which is a hyperbola.

⇒e=1+1632=32 and length of transverse axis

=82.

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Straight Lines 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 2018, covering the Straight Lines 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.