# Sphere equation from endpoints.

1. Sep 9, 2009

### graycolor

Find the equation of a sphere if one of its diameters has endpoints: (-19, -15, -3) and (1, 5, 17).

Thought it would be this, but the program web-work says its wrong.

Lets assume my first coordinate is a (-19, -15, -3) and b is (1, 5, 17)

I found the midpoint since I assumed that would be the center, then I found the length from my midpoint to b ,but my equation is wrong.

(x+9)^2+(y+5)^2+(z-7)^2-640=0

2. Sep 10, 2009

### lanedance

hey graycolor, method sounds right... showing your working will help finding the problem easier...

3. Sep 10, 2009

### njama

I think you calculated the radius wrong.

$$radius=diameter/2$$

$$diameter=\sqrt{(-19-1)^2+(-15-5)^2+(-3-17)^2}=\sqrt{3*20^2}=20\sqrt{3}$$

Now find the radius and then r2.

4. Sep 10, 2009

Thanks guys