Find the locus of a point which moves such that it distances from the point (0, 0) is thrice its distance from the y axis

Explanation

Let P(h, k) be the moving point whose locus we need to find :
Given |OP| = 3|PM|
`sqrt(h^2 + k^2) - |3h|`
`implies h^2 + k^2 = 9h^2`
`8h^2 - k^2 = 0` Hence locus of the point P is `8x^2 - y^2 = 0`