Determine the equation of each sphere, given that the center has the coordinates (3,-2,5)
The sphere touches the xy-plane at one point.
This is what it says in my solution book, which I don't get.
The radius of the sphere is the length of the perpendicular line dropped from the center of the xy-plane. Therefore, the radius is 5.
You said that the sphere touches the xy plane. Any point on the xy plane would have a z-coordinate of 0. If the sphere touches the xy-plane then it must do so at (3, -2, 0). The distance from the center to this point is 5, so that's why the radius is 5.