A point in the plane moves so that its distance from the origin is thrice its distance from the y-axis. Find i

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Puducherry TnboardTamil Nadu HSC First Year (DGE) Commerce Board 2022Subjective· 2mImportance★★★★★

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Set $\sqrt{x^2+y^2}=3|x|$ and square to get the locus $8x^2-y^2=0$ .

Let $P(x,y)$ be the moving point.

The condition is that the distance from the origin is thrice the distance from the $y$ -axis:

$\sqrt{x^2+y^2} = 3\,|x|$

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Q.A point in the plane moves so that its distance from the origin is thrice its distance from the $y$ -axis. Find its locus.