1. ## Radius of a sphere

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.

2. Originally Posted by chengbin
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.
Place a ball on your level writing table. How far its center from the table top?

3. I'm not sure if I get it.

Can someone explain it in more detail (a picture would be nice), or guide me to a place explaining this? I really suck in geometry.

4. Originally Posted by chengbin
I'm not sure if I get it.

Can someone explain it in more detail (a picture would be nice), or guide me to a place explaining this? I really suck in geometry.
the sphere's center is at the position (3,-2,5)

note that the center's z-coordinate is 5 ... that means the center is 5 units above the xy plane.

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.

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