The equation of a sphere is:
(x – h)^2 + (y – k)^2 + (z – l)^2 = r^2
where h, k and l are the coordinates of the center of the sphere
Using the midpoint formula, the coordinate of the center is:
h = (-4 + 6) / 2 = 1
k = (7 + -5) / 2 = 1
l = (6 + 7) / 2 = 6.5
so the equation becomes:
(x – 1)^2 + (y – 1)^2 + (z - 6.5)^2 = r^2
we plug in any point, in this case point P to solve for r:
(-4 -1)^2 + (7 – 1)^2 + (6 - 6.5)^2 = r^2
r^2 = 61.25
So the full equation is:
(x – 1)^2 + (y – 1)^2 + (z - 6.5)^2 = 61.25
