Math Help - Calc 3 Problem - Don't understand

1. Calc 3 Problem - Don't understand

Find the equations of the two spheres that are tangent with equal radii whose centers are (-3,1,2) and (5,-3,6).

I don't understand what it means when it says they are tangent with equal radii.

2. Originally Posted by tdat1979
Find the equations of the two spheres that are tangent with equal radii whose centers are (-3,1,2) and (5,-3,6).

I don't understand what it means when it says they are tangent with equal radii.
First, find the distance between the two centers:

$D=\sqrt{(5-(-3))^2+(-3-1)^2+(6-2)^2}=\sqrt{64+16+16}=\sqrt{96}=4\sqrt{6}$.

If you take $D$ and divide it by 2, you'll have two equal radii.

Thus, the equation of the spheres are $(x+3)^2+(y-1)^2+(z-2)^2=24$ and $(x-5)^2+(y+3)^2+(z-6)^2=24$

3. 24?
How did you get = 24? I don't understand where this number came from.

4. Originally Posted by inca2319
24?
How did you get = 24? I don't understand where this number came from.
The distance between the two centers is $4\sqrt{6}$. If they're to have the same radii, it would follow that $r=\frac{4\sqrt{6}}{2}=2\sqrt{6}$.

Thus, $r^2=2^2\cdot\sqrt{6}^2=4\cdot 6=24$...

5. Alright, I understand now. Thanks for the help!