Final answer:
The equation of the sphere is (x - 1)² + (y - 8)² + (z - 3)² = 94.
Step-by-step explanation:
To find the equation of the sphere, we can 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. In this case, the center is (1, 8, 3) and the point on the sphere is (4, 1, -3).
First, we can find the radius by calculating the distance between the center and the point using the distance formula:
r = sqrt((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)
Plugging in the values:
r = sqrt((4 - 1)² + (1 - 8)² + (-3 - 3)²)
r = sqrt(9 + 49 + 36)
r = sqrt(94)
Therefore, the equation of the sphere is:
(x - 1)² + (y - 8)² + (z - 3)² = 94