A series of hyperbola is drawn having a common transverse axis of length 2a. Prove that the locus of a 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), = 4x^(2) (x^(2) - a^(2))`.

A series of hyperbola are drawn having a common transverse axis of length 2 a.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 whose distance from the point (1,2) is equal to its distance from axis of y.

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

Find the locus of a point whose distance from x-axis is equal the distance from the point (1, -1, 2) :

The is a point P on the hyperbola (x^(2))/(16)-(y^(2))/(6)=1 such that its distance from the right directrix is the average of its distance from the two foci. Then the x-coordinate of P is

A hyperbola having the transverse axis of length sqrt2 units has the same focii as that of ellipse 3x^(2)+4y^(2)=12 , then its equation 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