Verified answer

Step 1: Find the midpoint of the diameter (this will be the center of the circle).

First find the midpoint of the segment that contains (−4, −4) and (12,14) as endpoints.

Midpoint formula

x_mid = [x1 + x2] / 2

y_mid = [y1 + y2] / 2

x_mid = -4 + 12 / 2 = 4

y_mid = -4 + 14 / 2 = 5

midpoint M is (4,5)

Step 2: Find the distance from the midpoint to one of the endpoints to find the length of the radius

I'm going to solve for r^2 using the square of the distance formula

Using the midpoint and an endpoint I get

r^2 = (12 - 4)^2 + (14 - 5)^2

= 64 + 81

= 145

Using the equation of a circle and the midpoint (4,5) we get

(x-4)^2 + (y-5)^2 = 145

Find mid point of (-4,-4)(12,14)

x1 + x2 / 2 = - 4 + 12 / 2 = 8/2 = 4

y1 + y2 / 2 = - 4 + 14 / 2 = 10/2 = 5

Centre of circle = (4,5)

Equation of circle = (x - 4)^2 + (y - 5)^2 = r^2

Find length of (-4- ,4) (12,14)

x2 - x1 = 12 - - 4 = 16

y2 - y1 = 14 - - 4 = 18

Sqrt(16^2 + 18^2 = Sqrt 256 + Sqrt324 = Sqrt580 = 24.01( that is a diameter)

Radius = 12

Equation of circle =(x - 4)^2 + (y - 5)^2 = 144

It looks like the circle you are describing would be (x-4)^2 + (y-5)^2 = 145

Or to rephrase, y = 5 +- sqr(145 - (x-4)^2)

The line segment for the diameter would be y = 9x/8 - 3.5

If (-4, -4) and (12, 14) are the endpoints of the diameter, then (4, 5) is the middle. ?((12 - 4)^2 + (14 - 5)^2) = ?(10^2 + 9^2) = ?181 is the radius (x - 4)^2 + (y - 5)^2 = 181 x^2 - 8x + sixteen + y^2 - 10y + 25 = 181 x^2 = y^2 - 8x - 10y - one hundred forty = 0 **