Equation of a Sphere

Date: 3 Jul 1995 23:14:03 -0400
From: Jason Crist
Subject: Equation for the graph of a sphere.

I was wondering what is the equation for a sphere on a graph with the 
dimensions x, y, and z?  Do you have to use calculus to solve a 
system for the intersection of such spheres? 

Thank you for your time.
JRC

Date: 13 Jul 1995 22:25:32 -0400
From: Dr. Ken
Subject: Re: Equation for the graph of a sphere.

Hey there!

The equation for a sphere of radius 1 with center at the origin is 
x^2 + y^2 + z^2 = 1.

In general, the equation for a sphere of radius R with center at (a,b,c) is
(x-a)^2 + (y-b)^2 + (z-c)^2 = R^2.

If you're looking at the intersection of two spheres, the intersection is
always a circle, and once you know that it's usually not too hard to figure
out what the circle is.  If, for instance, the two spheres are centered at
(a,b,c) and (A,B,C), then the circle of intersection will be in the plane 
(a-A)x + (b-B)y + (c-C)z = k for some constant k.  If you find just one
point that's common to both spheres, this will pinpoint k, and then you can
find the intersection of the plane and one of the spheres.

-K