Find an equation of the set of all points equidistant from the points A (-5, 6, 3) and B (3, 4, -8).
I didn't really know what to do on the first one. I took the midpoint of those two points to get the center = (-1, 5, -2.5). I then used the distance formula between the points A and B to get the diameter, then divided by 2 and squared and set it equal to the equation of the center. I also tried using the distance formula between what I got as the center and point A, which is the radius, and squaring it. It said both were wrong, which I figured, so I now don't know what to do.
Find the volume of the solid that lies inside both of the spheres:
x^2 + 18x + y^2 - 12y + z^2 + 40 = 0
x^2 + y^2 + z^2 = 81
For the second one, I completed the square for the first equation to get: (x+9)^2 + (y-6)^2 + (z+2)^2 = 81, the center is (-9, 6, -2) with R=9
x^2 + y^2 + z^2 = 81, the center is (0, 0, 0) with R=9
That's where I'm stuck at.
These are the last two from my homework exercises. There aren't any examples in the book like these so there isn't anything for me to follow.