IIT-JEE 2011 · Paper 2 · Mathematics Q48

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MathematicsSingle correct+3 / -1Question 48 of 60

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

x^2=y

y^2=2x

y^2=x

x^2=2y

Answer and worked solution

Official answer: C

Section point. $P=(h,k)=\left(\frac x4,\frac y4\right)$ , so $x=4h$ , $y=4k$ .

Locus. $(4k)^2=4(4h)$ , i.e. $k^2=h$ : $y^2=x$ .

(C)

Topics:Locus Parabola

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IIT-JEE 2011 · Paper 2, Mathematics question 48