Consider circle C with diameter DE.

The equation of the circle is ( ___)^2 + (___)^2 = ___.

The equation of the circle is (x -8)² + (y -4)² = 184.96

Step-by-step explanation:

In order to determine the equation of this circle we first need to calculate the coordinates of the center, which are given by the difference of the coordinates divided by two. We have:

Xc = [13 - (-3)]/2 = (13 + 3)/2 = 16/2 = 8

Yc = (11 - 3)/2 = 8/2 = 4

Therefore the center is (8,4). We now need to find the radius of the circle, which is given by the distance from the center to one of the points given:

r = sqrt{[8 - (-3)]² + (11 - 3)²} = sqrt(11² + 8²) = 13.60

The equation of a circle is given by:

(x - Xc)² + (y - Yc)² = r²

(x -8)² + (y -4)² = (13.6)²

(x -8)² + (y -4)² = 184.96

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step-by-step explanation: