JEE Main 2018MathematicsParabolaMediumMCQ

JEE Main 2018 — Parabola Question with Solution

JEE Main 2018 (16 Apr Online)

Question

Let P be a point on the parabola x2=4y. If the distance of P from the center of the circle x2+y2+6x+8=0 is minimum, then the equation of the tangent to the parabola at P is

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Show full solutionCorrect option: A
Correct answer
Ax+y+1=0

Step-by-step explanation

Let P2t,t2.

Equation normal at P to x2=4y be

y-t2=-1tx-2t.

It passes a normal through -3,0.

⇒0-t2=-1t-3-2t

⇒t3+2t+3=0

⇒t+1t2-t+3=0

⇒t=-1

So, point P is -2,1.

Equation of a tangent to x2=4y at -2,1.

⇒x-2=2y+1

∴x+y+1=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.