Question

(1 point) find the equation of the sphere centered at (−9,4,1)(−9,4,1) with radius 4. normalize your equations so that the coefficient of x2x2 is 1. equation editorequation editor = 0. give an equation which describes the intersection of this sphere with the plane z=2z=2. equation editorequation editor = 0.\

Answer 1

The equation of a sphere centered at (h, j, k) with radius r is

... (x -h)² +(y -j)² +(z -k)² = r²

Your sphere has center (-9, 4, 1) and radius 4, so its equation is

... (x +9)² +(y -4)² +(z -1)² = 16

This can be written in general form as

... x² + y² + z² +18x -8y -2z +82 = 0