Answer:
(x +3)^2 + (y +3)^2 = 61
Step-by-step explanation:
The standard form equation of a circle with center (h, k) and radius r is ...
(x -h)^2 + (y -k)^2 = r^2
So, to write the desired equation, we need to know the center of the circle and its radius.
The center is the midpoint of the diameter, so is the average of the endpoints:
((2, 3) +(-8, -9))/2 = ((2-8)/2, (3-9)/2) = (-6/2, -6/2) = (-3, -3)
The radius can be found using the distance formula to find the distance between the circle center and either of the diameter end points.
d = √((x2 -x1)^2 +(y2 -y1)^2)
r = √((-3-2)^2 +(-3-3)^2) = √(25+36) = √61
Then ...
- (h, k) = (-3, -3)
- r^2 = (√61)^2 = 61
so the desired equation is ...
(x +3)^2 + (y +3)^2 = 61
