1 2 3 10 Find the equation of the sphere that passes through the origin and center at (3,2,1). Solution: We know the center, so the equation of the sphere must be (aa) + (y - b) + (z c) = d, where a type your answer type your answer... and d is unknown. , c= type your answer.... ,b= We only need to find the d (or the square of the radius) to fully determine the sphere. The other condition "pass through the origin" should be utilized for this purpose. Since (0,0,0) is on the sphere, plug it into the equation we can easily get d= type your answer... thus uniquely determine the sphere.

Find the equation of the sptivere that passes through the origin and center at (3,2,1) Solution: We know the center, so the equation of the sphere must be (xa)2+(yb)2+(zc)2=d, where an and dis unknown. We only need to find the d (or the square of the radius) to fully determine the sphere. The other condition "pass through the origin" shouid be utilized for this purpose. Since (0,0,0) is on the sphere, plug it into the equation we can easily get d= thus uniquely determine the sphere