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.