Question

Find the equation of a sphere if one of its diameters has endpoints: (-17, -2, -15) and (-1, 14, 1).

Answer 1

The distance between the two given points is the diameter. Cut that in half and you get the radius.

To find the center, you can find the midpoint of the given points.

Answer 2

I thought that it was (x+9)^2+(y-6)^2+(z+7)^2-64=0. But WebWork said it's wrong.

Answer 3

Help? Please? I need help really bad!

Answer 4

Never mind. Figured it out. It's -192, not -64.

Answer 5

If you have two points \((a_1,\ldots,a_n)\) and \((b_1,\ldots,b_n)\), the distance between these points is
\[d=\sqrt{(a_1-b_1)^2+\cdots+(a_n-b_n)^2}\]
In this case, you have
\[\begin{matrix}
a_1=-17&&b_1=-1\\
a_2=-2&&b_2=14\\
a_3=-15&&b_3=1
\end{matrix}\]
So the length of the diameter (the distance between the two points) is
\[d=\sqrt{(-17+1)^2+(-2-14)^2+(-15-1)^2}=\sqrt{768}=16\sqrt3\]
which means the radius is \(r=8\sqrt3\), giving \(r^2=64\times3=192\).

Answer 6

Your center is correct though.