The equation of circle having diameter with endpoints (-2,1) and (6,7) is

(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

Step-by-step explanation: