(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Reflection of surface about a plane

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