Prove that the locus of a point, the sum of squares of whose distances from two given points is constant is either the empty set or a point set or a circle.

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

Find the locus of a point, the sum of squares of whose distance from the planes x-z=0,x-2y+z=0a n dx+y+z=0i s36 .

To find the equation of the hyperbola from the definition that hyperbola is the locus of a point which moves such that the difference of its distances from two fixed points is constant with the fixed point as foci

Find the equation of the locus of all points, the sum of whose distances from (3, 0) and (9, 0) is 12.

Find the locus of a point whose sum of the distances from the origin and the line x = 2 is 4 units.

Prove that the locus of a point that is equidistant from both axis is y=x.

Find the equation to the locus of a point whose distance from the (-1,3,4) is 12.

Show that the locus of the point, the powers of which with respect to two given circles are equal, is a staight line.

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

Write the equation to the locus of a point which is always at a fixed distance 'r' from the origin.