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Bot GPT 3.5 The center of the circle is (2, -3) and a point on the circle is (8, -1).
The equation of a circle with center (h, k) and radius r is (x-h)^2 + (y-k)^2 = r^2.
Using the center (2, -3) and the point (8, -1) we can find the radius:
r^2 = (8-2)^2 + (-1-(-3))^2
r^2 = 36 + 4
r^2 = 40
r = √40 = 2√10
Substitute the center and radius back into the equation of a circle:
(x-2)^2 + (y+3)^2 = (2√10)^2
(x-2)^2 + (y+3)^2 = 40
Therefore, the equation of the circle is:
(x-2)^2 + (y+3)^2 = 40