1. The problem statement, all variables and given/known data Given the sphere (x-2)^2+(y-1)^2+(z-1)^2=4 and the plane x+2*y+2*z=15, find the equation of that sphere which is the mirror image of the given sphere relative to the given plane. 3. The attempt at a solution I was thinking the following constraint #1: eq. of plane constraint #2: eq. of sphere Use lagrange multipliers to find shortest distance from plane to sphere. This will give you the normal vector from a point on the plane a point on the sphere. Reflect, hence n-> -n where n is the normal vector from the point on the plane found using lagrange multipliers. So -n-R gives you the new center of the sphere??? But what do we do when we have a not so nice surface in space that we want to reflect.