Answer:
(x+10)² + (y-8)² = 41
Explanation:
First, we find the length of the diameter.
from distance formula, d = SQR ROOT OF [(-14+6)² + (13-3)²]
diameter = SQR ROOT OF [8² + 10²] = √164 = √4√41 = 2√41
***** so the radius is half that, r =√41
The center of the circle is at the midpoint of the diamater.
x = (1/2)(-6 + -14) = (1/2)(-20) = -10
y = (1/2)(3 + 13) = (1/2)(16) = 8
center (h,k) = (-10,8)
circle equation: (x-h)² + (y-k)² = r²
(x- -10)² + (y - 8)² = (√41)²
(x+10)² + (y-8)² = 41
Sorry it took a while.