Answer:
(x − 2)² + (y − 4)² = 25
Step-by-step explanation:
The center of the circle is the midpoint of the diameter, and the radius of the circle is half the length of the diameter.
Finding the center:
h = (x₁ + x₂) / 2
h = (-2 + 6) / 2
h = 2
k = (y₁ + y₂) / 2
k = (1 + 7) / 2
k = 4
(h, k) = (2, 4)
Finding the radius:
d = √((x₁ − x₂)² + (y₁ − y₂)²)
d = √((-2 − 6)² + (1 − 7)²)
d = √((-8)² + (-6)²)
d = √(64 + 36)
d = √100
d = 10
d/2 = 5
r = 5
So the equation of the circle is:
(x − h)² + (y − k)² = r²
(x − 2)² + (y − 4)² = 25
