Equation of a sphere and geometric plane

Question

Problem:

Equation of a Sphere and Geometric Plane

a) Find the equation of the sphere that go through the points (1, -3, 4), (1, -5, 2) and (1, -3, 0) and has its center in plane x + y + z = 0

Solution must be:                 x²+y²+z²-2x+6y-4z+10=0

b) Find the geometric place of the points whose sum of squares of its distances to the planes x+4y+2z=0, 2x -y+z=0 y 2x +y-3z = 0 is equal to 10

Solution must be:                 x²+y²+z²=10

5) Study and represent the following ellipsoids

                                             a) 8x² + 2y² +9z² 100
                                             b) x² + 4y² +4z²-12x =0