JEE Main 2020MathematicsParabolaHardMCQ

JEE Main 2020 — Parabola Question with Solution

JEE Main 2020 (06 Sep Shift 2)

Question

The centre of the circle passing through the point 0, 1 and touching the parabola y=x2 at the point 2, 4 is :

Choose an option

Show full solutionCorrect option: D
Correct answer
D-165, 5310

Step-by-step explanation

y=x2

Tangent at 2,4 is 12y+4=2x, using Cartesian form.

⇒4x-y-4=0

Equation of circle

x-22+y-42+λ4x-y-4=0

It passes through 0,1

∴ 4+9+λ0-1-4=0

13=5λ⇒λ=135

∴Circle is x2-4x+4+y2-8y+16+1354x-y-4=0

⇒x2+y2+525-4x-8+135y+20-525=0

⇒x2+y2+325x-535y+485=0

∴ Centre is -165,5310

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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.