Answer:
(x +1)² +(y -5)² = 65
Step-by-step explanation:
The center is the midpoint of the diameter, the average of the end points:
C = ((7, 4) +(-9, 6))/2 = ((7-9)/2, (4+6)/2) = (-1, 5)
The formula for center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
We can find r² by substituting one of the diameter end points for (x, y) and the center for (h, k).
(7 +1)² +(4 -5)² = r² = 65
Then the circle's equation is ...
(x +1)² +(y -5)² = 65
