A point moves so that its distance from the point `(-2, 3)` is always three times its distance from the point `(0, 3)`. Find the equation to its locus.

A fixed point is at a perpendicular distance a from a fixed straight line and a point moves so that its distance from the fixed point is always equal to its distance from the fixed line.Find the equation to its locus,the axes of coordinates being drawn through the fixed point and being parallel and perpendicular to the given line.

A point moves so that square of its distance from the point (3,-2) is numerically equal to its distance from the line 5x-12y=3 . The equation of its locus is ..........

A point moves such teat its distance from the point (4,0) is half that of its distance from the line x=16, find its locus.

A point moves so that its distance from the point (2,0) is always (1)/(3) of its distances from the line x-18 . If the locus of the points is a conic, then length of its latus rectum is

The equation of the locus of a point which moves so that its distance from the point (ak, 0) is k times its distance from the point ((a)/(k),0) (k ne 1) is

A point P(x,y) moves in the xy-plane in such a way that its distance from the point (0,4) is equal to (2)/(3)rd of its distancefrom the x -axis find the equation to the locus of P.

A point P is such that its perpendicular distance from the line y – 2x + 1 = 0 is equal to its distance from the origin. Find the equation of the locus of the point P.