Intersection of Two Spheres
For quite sometime I have been intrigued by the curve created by the intersection of two spheres with the following properties/conditions:
Let both spheres have the same radius. Let's say a radius of 2.
Let one sphere be centered at (0,0,0) and the other sphere be centered at
I think the equations for the two spheres are:
I have seen a method finding the intersection when both spheres have the same coordinates on the y and z axis and differing coordinates on the x axis. This involves combining the two equations and solving for x.
This would yield a circle parallel to the yz plane.
So, here is what I did:
Multiplying through and rearranging I got
I think this is the equation of the plane where the two spheres intersect.
I am not sure what to do next.
I have read that it will be a circle and that there will be two equations describing the curve.(Now that i think about it i guess the intersection of 2 spheres will always be a circle)
I had built a model about 10 years ago out of balsa wood and the curve really did not look circular. But maybe that was due to the inaccuracies of the model.
How do I find an equation that describes this curve.
I looked in my old calculus book but could find nothing. :(
Any help would be greatly appreciated.