Find an equation of the sphere with center (2, -6, 4) and radius 5. Describe its intersection with the each of the coordinate planes.
Equation of a sphere with three dimensions X2 + Y2 + Z2 = R2
The Attempt at a Solution
My equation is (x - 2)2 + (y + 6)2 + (z - 4)2 = 25
This sphere intersects the XY plane by making a circle with radius 3 and it intersects the YZ plane with a radius of (21)0.5. However, my equation for the XZ plane came out to be negative. That is, Radius squared is less than zero. Does that mean the sphere doesn't intersect the XZ plane?