A point moves so that its distance from y-axis is half of its distance from the origin. Find the locus of the point.

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Solution

$x = \frac{1}{2} \sqrt{x^{2} + y^{2}}$
$\Rightarrow 2 x = \sqrt{x^{2} + y^{2}}$
$\Rightarrow 4 x^{2} = x^{2} + y^{2}$
$\Rightarrow 3 x^{2} - y^{2} = 0$

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