Question

A sphere of radius 9 is centered at the point (-3,-2,-1). What are the coordinates of the two points where the surface of the sphere intersects the Z-axis?

Answer 1

sphere equation :
(x+3)^2 + (y+2)^2 + (z+1)^2 = 81
z intersection means both Y and X equal zero
plug it into the equation gives :
9 + 4 + z^2 + 2z + 1 = 81
z^2 + 2z - 67 = 0

quadratic formula gives you :
7.246
-9.246