JEE Main 2018MathematicsParabolaHardMCQ

JEE Main 2018 — Parabola Question with Solution

JEE Main 2018 (15 Apr)

Question

Two parabolas with a common vertex and with axes along the x-axis and y-axis respectively, intersect each other in the first quadrant. If the length of the latus rectum of each parabola is 3, then the equation of the common tangent to the two parabolas is :

Choose an option

Show full solutionCorrect option: D
Correct answer
D4x+y+3=0

Step-by-step explanation

Equation of two parabola are y2=3x and x2=3y.

Let equation of tangent to y2=3x is y=mx+34m is also tangent to x2=3y

⇒ x2=3mx+94m

⇒4mx2-12m2x-9=0 have equal roots

⇒D=0

⇒144m4=44m(-9)

⇒m4+m=0⇒m=-1

Hence, common tangent is y=-x-34

⇒4x+y+3=0

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About this question

This is a previous-year question from JEE Main 2018, covering the Parabola 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.