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

Answer 1

you know that a sphere with center at (0,0,0) is x^2 + y^2 + z^2 = 25
So, shift the center and you have
(x-2)^2 + (y+6)^2 + (z-4)^2 = 25
To find the intersection with the xy plane, set z=0 and you have
(x-2)^2 + (y+6)^2 + (0-4)^2 = 25
(x-2)^2 + (y+6)^2 + 16 = 25
(x-2)^2 + (y+6)^2 = 9
So, it's a circle of radius 3 with center at (2,-6)

and so on for the other planes.