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

3 x^{2} - y^{2} = 0

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3 x^{2} + y^{2} = 0

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x^{2} - y^{2} = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x^{2} + y^{2} = 0

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Solution

The correct option is C $3 x^{2} - y^{2} = 0$
R.E.F image
distance from origin is $\sqrt{x^{2} + y^{2}}$
$x = \frac{1}{2} \sqrt{x^{2} + y^{2}} \Rightarrow 4 x^{2} = x^{2} + y^{2}$
$\Rightarrow 3 x^{2} - y^{2} = 0$

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