JEE Main 2020MathematicsParabolaMediumMCQ

JEE Main 2020 — Parabola Question with Solution

JEE Main 2020 (05 Sep Shift 1)

Question

If the common tangent to the parabolas, y2=4 x and x2=4 y also touches the circle, x2+y2=c2, then c is equal to :

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Show full solutionCorrect option: B
Correct answer
B12

Step-by-step explanation

Given: y2=4x&x2=4y

Comparing with standard equations, y2=4a1x & x2=4a2y, a1=a2=1

Therefore tangent of y2=4x is y=mx+1m which is also tangent to x2=4y, whose equation would be y=mx-m2

∴  1m=-m2⇒  m=-1

∴ common tangent is y=-x-1, which touches x2+y2=c2

∴ (-1)2=c2(1+(-1)2)⇒ 1=c2·(1+1)⇒c2=12

 

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About this question

This is a previous-year question from JEE Main 2020, 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.