Find an equation of the sphere with center (2, -6, 4) and radius 5. describe its intersection with each of the coordinate planes

Since this is a 3D object, the center of the sphere has 3 coordinates:  x=2, y = -6 and z = 4.

The equation would be:

(x-2)^2 + (y+6)^2 + (z-4)^2 = 5^2 (answer).

To find the equation of the intersection of this sphere with the xy plane, let z = 0.  Then (x-2)^2 + (y+6)^2 + (0-4)^2 = 25

This simplifies to (x-2)^2 + (y+6)^2 = 5^2 (or 25).

Find and describe the sphere's intersections with the other 2 coord. planes.

Ibelieve the answer is c