JEE Main 2015MathematicsParabolaLocuseasyMCQ

JEE Main 2015 — Parabola Question with Solution

From: JEE Main 2015 (Offline)

Question

Let be the vertex and be any point on the parabola, . If the point divides the line segment internally in the ratio , then locus of is :

Choose an option

Show full solutionCorrect option: B
Correct answer
B

Step-by-step explanation

Let the coordinates of Q and P be (x1, y1) and (h, k) respectively.

Q lies on x2 = 8y,

x = 8y ....... (1)

Again, P divides OQ internally in the ratio 1 : 3.

or x1 = 4h and

or y1 = 4k

JEE Main 2015 (Offline) Mathematics - Parabola Question 127 English Explanation

Now putting x1 and y1 in (1) we get,

16h2 = 32k or, h2 = 2k

the locus of P is given by, x2 = 2y.

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Parabola chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

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.