Answer:
Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is .
Step-by-step explanation:
There are two kew parameters for a sphere: Center (,
,
) and Radius (
). The radius is the midpoint of the line segment between endpoints. That is:
The radius can be found by halving the length of diameter, which can be determined by knowning location of endpoints and using Pythagorean Theorem:
The general formula of a sphere centered at (h, k, s) and with a radius r is:
Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is .