JEE Main 2015MathematicsParabolaMediumMCQ

JEE Main 2015 — Parabola Question with Solution

JEE Main 2015 (04 Apr)

Question

Let O be the vertex and Q be any point on the parabola, x2=8y. If the point P divides the line segment OQ internally in the ratio 1:3, then the locus of P is

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Show full solutionCorrect option: A
Correct answer
Ax2=2y

Step-by-step explanation

General point on x2=8y is Q4t,2t2

Let Ph,k divide OQ in ratio 1:3

h,k=14t+301+3,12t2+301+3

h,k=t,2t24

h=t & k=t22

k=h22

⇒  x2=2y  is the required locus. 

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About this question

This is a previous-year question from JEE Main 2015, 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.