Question

Find an equation of a sphere if one of its diameters has endpoints (2, 4, 5) and (6, 8, 9).

Answer 1

First use distance formula to find radius of sphere:

`d = √((x_2 -x_1)^2 + (y_2 - y_1)^2 + (z_2 -z_1)^2) \\ \\ d = √((6-2)^2 + (8-4)^2 + (9-5)^2) \\ \\ d = √(4^2 +4^2 +4^2) \\ \\ d = 4 √(3) \\ \\ r =(d)/(2) = 2 √(3)`

Next, find center of sphere.
The center is located at midpoint between given endponts.

`center = ((2+6)/(2), (4+8)/(2),(5+9)/(2)) \\ \\ center = (4,6,7)`

Finally enter values into general equation of sphere:

`(x-a)^2 + (y-b)^2 + (z-c)^2 = r^2 \\ \\ (x-4)^2 + (y-6)^2 + (z-7)^2 = 12`