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 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 such that its distance from the point (0,-1) is twice its distance from the line 3x+4y+1=0

Find the locus of a point, which moves so that its distance from (1, 2, 3) is four times its distance from YZ-plane.

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

If a point moves such that twice its distance from the axis of x exceeds its distance from the axis of y by 2, then its locus is

The locus of a point which moves so that the difference of the squares of its distance from two given points is constant, is a

The eccentricity of the hyperbola whose latus rectum is half of its transverse axis is:

A hyperbola having the transverse axis of length 2 sin theta is confocal with the ellipse 3x^(2)+4y^(2)=12. Then its equation is