Question

Consider again the sphere of radius 5 centered at (2, 3,−6). Describe the intersection of the sphere with the xz-plane. Write an equation (or equations) for this curve.

Answer 1

Isn't the equation
(x-2)^2 + (y-3)^2 + (z+6)^2 = 25

And on the x-z plane, isn't y = 0 ?
so
(x-2)^2 + (0-3)^2 + (z+6)^2 = 25
(x-2)^2 + (z+6)^2 = 25 + 9
(x-2)^2 + (z+6)^2 = 34

take it from there.

Answer 2

Reiny, I can't