A circle of radius 2 is contained in the plane y=3.

A circle of radius 4 is contained in the plane y=7.

Both circles lie on the surface of a sphere.

What is the radius of the sphere?

i changed it to the y= 0 and y = 4 planes. then imagine the circles have centers at (0,0,0) and (0,4,0). And given the radii of these we can imagine a cirlce with the same radius of the sphere that is projected on the z - plane with equation x^2 + (y-k)^2 = r^2. And we have two points - (2,0) and (4,4). The left side of the eqn must be equal for each pair of pts so
4+k^2 = 16 + (4-k)^2
k = 7/2

back to the eqn using (2,0)

r = sqrt(65)/2

Posted by vectorboy on 2004-08-26 22:34:25