Answer:
(x - 3)² + (y + 1)² = 65
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 centre C is at the midpoint of the endpoints of the diameter.
Using the midpoint formula to find C
C = (
,
) = (
,
) = (3, - 1 )
The radius is the distance from the centre to either of the endpoints of the diameter.
Using the distance formula to find r
with C (3, - 1 ) and (7, 6 ) , then
r =
=
=
=
Then equation of circle is
(x - 3)² + (y - (- 1) )² = (
)², that is
(x - 3)² + (y + 1)² = 65 ← equation of circle