Find the equation of the locus of a point such that the sum of its distances from two fixed points is constant and equal to 2 c.

Find the equation of the set of points such that the sum of its distances from (0, 2) and (0, - 2) is 6.

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

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 a point which moves so that the difference of its distances from the points (3, 0) and (-3, 0) is 4 units.

Find the equation of the locus of all points such that the difference of their distances from (4, 0) and (-4, 0) is always equal to 2.

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

Find the equation of the locus of the points twice as from (-a, 0) as from (a, 0).

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

Find the equation of the set of points P such that its distances from the points A (3, 4, - 5) and B (- 2, 1, 4) are equal.

A circle is the locus of a point in a plane such that its distance from a fixed point in the plane is constant. Anologously, a sphere is the locus of a point in space such that its distance from a fixed point in space in constant. The fixed point is called the centre and the constant distance is called the radius of the circle/sphere. In anology with the equation of the circle |z-c|=a , the equation of a sphere of radius is |r-c|=a , where c is the position vector of the centre and r is the position vector of any point on the surface of the sphere. In Cartesian system, the equation of the sphere, with centre at (-g, -f, -h) is x^2+y^2+z^2+2gx+2fy+2hz+c=0 and its radius is sqrt(f^2+g^2+h^2-c) . Q. Radius of the sphere, with (2, -3, 4) and (-5, 6, -7) as xtremities of a diameter, is