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:
$\displaystyle D=\sqrt{(5-(-3))^2+(-3-1)^2+(6-2)^2}=\sqrt{64+16+16}=\sqrt{96}=4\sqrt{6}$.
If you take $\displaystyle D$ and divide it by 2, you'll have two equal radii.
Thus, the equation of the spheres are $\displaystyle (x+3)^2+(y-1)^2+(z-2)^2=24$ and $\displaystyle (x-5)^2+(y+3)^2+(z-6)^2=24$