Let (x, y) be any point on the parabola y^2 = | vedclass

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(C) Let the coordinates of $P$ be $(h, k)$.Since $P$ divides the line segment joining $(0, 0)$ and $(x, y)$ in the ratio $1:3$,by the section formula,

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$y^2 = x$

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(C) Let the coordinates of $P$ be $(h, k)$.Since $P$ divides the line segment joining $(0, 0)$ and $(x, y)$ in the ratio $1:3$,by the section formula,the coordinates of $P$ are given by:$h = \frac{1 \cdot x + 3 \cdot 0}{1 + 3} = \frac{x}{4}$$k = \frac{1 \cdot y + 3 \cdot 0}{1 + 3} = \frac{y}{4}$Thus,$x = 4h$ and $y = 4k$.Since the point $(x, y)$ lies on the parabola $y^2 = 4x$,we substitute the values of $x$ and $y$:$(4k)^2 = 4(4h)$$16k^2 = 16h$$k^2 = h$Replacing $(h, k)$ with $(x, y)$,the locus of $P$ is $y^2 = x$.

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

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