Question

An equation of the sphere that passes through the origin and has its center at (4, 2, 2) is:

(x - 4)^2 + (y - 2)^2 + (z - 2)^2 = 24

Answer 1

The equation of the sphere that passes through the origin and has its center at (4, 2, 2) is (x - 4)^2 + (y - 2)^2 + (z - 2)^2 = 24.

Step-by-step explanation:

The equation of the sphere that passes through the origin and has its center at (4, 2, 2) is:

(x - 4)2 + (y - 2)2 + (z - 2)2 = 24

To find the equation of a sphere, we use the formula (x - h)2 + (y - k)2 + (z - l)2 = r2, where (h, k, l) is the center of the sphere and r is the radius. Since the sphere passes through the origin, the center is (0, 0, 0) and the equation simplifies to:

x2 + y2 + z2 = 24