# Sphere Intersects with Plane

1. Jan 24, 2010

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?

2. Jan 25, 2010

### 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:
$$(x-3)^2 + (y-2)^2 + (z+5)^2 = 36$$
$$x=0$$
$$y=0$$