Question

Consider circle C with diameter DE.

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

Answer 1

I did the math myself, and the options are: x-5, y-7, and 80

Hope this helps, I'm 80% sure this is right so don't trust me too much.

Answer 2

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

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