Answer:
(x - 2)² + (y - 7)² = 26
Explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
The coordinates of the centre are at the midpoint of the endpoints of the diameter and the radius is the distance from the centre to either of the 2 endpoints
Find the centre using the midpoint formula
centre = [
(- 3 + 7),
(8 + 6)] = (2, 7)
to find the radius use the distance formula
r = √(x₂ - x₁)² + (y₂ - y₁)²
with (x₁, y₁ ) = 2, 7) and (x₂, y₂ ) = (7, 6)
r =
=
=
centre (2, 7 ) and r² = (
)² = 26, hence
(x - 2)² + (y - 7)² = 26 ← equation of circle