Name the locus of the point P, sum of whose distances from two fixed points `F_1(0,0) and F_2(3,4)` is constant equal to 6.

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

Find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (- 4, 0, 0) is equal to 10.

The sum of the squares of the distances of a moving point from two fixed points (a,0) and (-a ,0) is equal to a constant quantity 2c^2 . Find the equation to its locus.

Find the equation of the set of points P, the sum of whose distance from A(4,0,0) and B(-4,0,0) is equal to 10.

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

Find the vector equations to the locus of a point whose distance from the point C(alphahati+betahatj+gammahatk) is constant equal to a.

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.

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. The centre of the sphere (x-4)(x+4)+(y-3)(y+3)+z^2=0 is

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

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