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JEE Advanced 2011Paper 2

Exam: JEE Advanced
Year: 2011
Paper: Paper 2
Subject: Mathematics
Chapter: Parabola

JEE Advanced 2011 · Paper 2 · Mathematics · Parabola

Let (x, y) be any point on the parabola y^2=4 x . Let P be the...

Let

(x, y)

be any point on the parabola

y^2=4 x

. Let

P

be the point that divides the line segment from

(0,0)

to

(x, y)

in the ratio

1: 3

. Then, the locus of

P

is

Let (x, y) be any point on the parabola y^2=4 x . Let P be the point that divides the line segment from (0,0) to (x, y)

Let (x, y) be any point on the parabola y^2=4 x . Let P be the point that divides the line segment from (0,0) to (x, y)

Options

A $x^2=y$
B $y^2=2 x$
C $y^2=x$
D $x^2=2 y$

Correct answer

C. $y^2=x$

Step-by-step solution

\text{ By section formula, }<img src="/api/proxy-image?url=https%3A%2F%2Ffirebasestorage.googleapis.com%2Fv0%2Fb%2Fquantrexacademy-app.firebasestorage.app%2Fo%2Fquestions%252Ffigs%252Fpyq%252Fjee_advanced%252FNZeJW46lYjK_Tb4Ljhd5REr04ncqMpNoSecFzLx2gXo.original.fullsize.png%3Falt%3Dmedia&clean=1&v=wm2" data-qx-orig-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fjee_advanced%2FNZeJW46lYjK_Tb4Ljhd5REr04ncqMpNoSecFzLx2gXo.original.fullsize.png?alt=media" data-qx-storage-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fjee_advanced%2FNZeJW46lYjK_Tb4Ljhd5REr04ncqMpNoSecFzLx2gXo.original.fullsize.png?alt=media">

\\

h=\frac{x+0}{4}, k=\frac{y+0}{4}\therefore \quad x=4 h

and

y=4 k

Substituting in

y^2=4 x

,

(4 k)^2=4(4 h) \Rightarrow k^2=h

or

y^2=x

is required locus.

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