How Does a Sphere Intersect Each Coordinate Plane and Axis?

[Theansweris42]

I have a sphere with the equation
(x-3)²+(y-2)²+(z+5)²=36

two question:
1. how do I find the equation of the shapes where the surface intersects each coordinate plane.
2. How do I find the points where the surface intersects each coordinate axis.

I think for 1. that it will be a circle but how do I find the equation of that circle? What part of the sphere equation do I need to set to zero?

 

[rasmhop]

A point (x,y,z) is in both the sphere and the yz-plane iff:
(x-3)^2 + (y-2)^2 + (z+5)^2 = 36
x=0
So just substitute x=0 in the sphere equation to get a circle equation. For the intersection with the z-axis we have:
(x-3)^2 + (y-2)^2 + (z+5)^2 = 36
x=0
y=0