Find the locus of a point which moves such th | vedclass

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Question

(A) Let $P(h, k)$ be the moving point whose locus is required.According to the given condition,the distance of $P$ from the origin $O(0, 0)$ is twice

Vedclass · Accepted Answer

$3x^2 - y^2 = 0$

Vedclass · Answer

(A) Let $P(h, k)$ be the moving point whose locus is required.According to the given condition,the distance of $P$ from the origin $O(0, 0)$ is twice its distance from the $y$-axis.The distance of $P(h, k)$ from $O(0, 0)$ is $\sqrt{h^2 + k^2}$.The distance of $P(h, k)$ from the $y$-axis is $|h|$.So,$\sqrt{h^2 + k^2} = 2|h|$.Squaring both sides,we get:$h^2 + k^2 = 4h^2$$k^2 = 3h^2$$3h^2 - k^2 = 0$.Replacing $(h, k)$ with $(x, y)$,the locus is $3x^2 - y^2 = 0$.

Find the locus of a point which moves such that its distance from the point $(0, 0)$ is twice its distance from the $y$-axis.

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