Question

Find an equation of a sphere if one of its diameters has endpoints (3, 2, 5) and (5, 6, 7). Incorrect: your answer is incorrect.

Answer 1

use midpoint equation

radius = distance between midpoint and one of the endpoints.

midpoint: (3+5)/2, (2+6)/2, (5+7)/2 = (4,4,6)

equation of sphere: (x-4)^2 + (y-4)^2 + (z-6)^2 = r^2

square distance between midpoint and one of the endpoints.

r^2 = 6

Equation: (x-4)^2 + (y-4)^2 + (z-6)^2 = 6