A series of hyperbola is drawn having a common transverse axis of length 2a. Then the locus of a point P on each hyperbola, such that its distance from the transverse axis is equal to its distance from an asymptotes, is

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

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 such that its distance from the origin is three times its distance from x-axis.

Find the locus of the point such that its distance from the x-axis is half its distance from the y-axis.

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 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 whose distance from (a, 0) is equal to its distance from the 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 locus of a point so that its distance from the axis of x is always one half its distance from the origin.

Find the equation of the locus of a point whose distanace from the z-axis is equal to its distance from the xy-plane.