Answer:
(x + 1)² + (y − 3)² = 41
Step-by-step explanation:
The center of the circle is the midpoint of the diameter.
(h, k) = ((x₂ + x₁)/2, (y₂ + y₁)/2)
(h, k) = ((3 + -5)/2, (-2 + 8)/2)
(h, k) = (-1, 3)
The radius is half the length of the diameter.
r = ½ √((x₂ − x₁)² + (y₂ − y₁)²)
r = ½ √((3 − -5)² + (-2 − 8)²)
r = ½ √(8² + 10²)
r = √41
Therefore, the equation of the circle is:
(x − h)² + (y − k)² = r²
(x + 1)² + (y − 3)² = 41
