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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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Verified Answer
The correct answer is:
$y^2=x$
$y^2=x$
$$
\text { By section formula, }
$$
$h=\frac{x+0}{4}, k=\frac{y+0}{4}$
$\therefore \quad x=4 h$ 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.
\text { By section formula, }
$$
$h=\frac{x+0}{4}, k=\frac{y+0}{4}$
$\therefore \quad x=4 h$ 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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