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  4. Let (x, y) be any point on the parabola y2=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

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Q. 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

JEE AdvancedJEE Advanced 2011

Solution:

$y^{2}=4 x$
and $Q$ will lie on it
$\Rightarrow (4 k)^{2}=4 \times 4 h$
$\Rightarrow k^{2}=h$
$\Rightarrow y^{2}=x$ (replacing h by x and k by y)

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