Find the locus of a point which moves such that its distance from the origin is three times its distance from x-axis.

Find the locus of a point which moves such that its distance from x axis is five times its distance from y axis.

Find the locus of a point which moves so that its distance from the x-axis is twice its distance from the y-axis.

Find the locus of a point , which moves such that its distance from the point (0,-1) is twice its distance from the line 3x+4y+1=0

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

Find the locus of a point P which moves such that its distance from the line y=sqrt(3)x-7 is the same as its distance from (2sqrt(3),-1)

Find the locus of a point P which moves such that its distance from the line y=sqrt(3)x-7 is the same as its distance from (2sqrt(3),-1)

Find the equation of the locus of a point which moves so that its distance from the x-axis is double of its distance from the y-axis.

Find the locus of the point such that its distance from the y-axis is equal to its distance from the point (1, 1).

Find the locus of a point which moves so that its distances from the points (3,4,-5) and (-2,1,4) are equal.

A series of hyperbola are drawn having a common transverse axis of length 2a. Prove that the locus of point P on each hyperbola, such that its distance from the transverse axis is equal to its distance from an asymptote, is the curve (x^2-y^2)^2 =lambda x^2 (x^2-a^2), then lambda equals