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

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Aicharya · Accepted Answer

$ 	ext { By section formula, } $ $h=\frac{x+0}{4}, k=\frac{y+0}{4}$ $	herefore \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

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

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