Answer:
The radius is 4 units, and the equation of the circle is:
(x - 3)^2 + (y + 5)^2 = 16
Explanation:
A circle centered at the point (a, b) and with a radius R, is written as:
(x - a)^2 + (y - b)^2 = R^2
In the image, we can see that a segment that cuts the circle in two halves is the segment between the points:
(-1, -5) and (7, - 5)
The distance between these points is the diameter of the circle.
Remember that the distance between two points (x₁, y₁) and (x₂, y₂) is:
D = √( (x₂ - x₁)^2 + (y₂ - y₁)^2)
Then in this case, the distance between the known points is:
D = √( (7 - (-1))^2 + (-5 - (-5))^2)
D = √( 8^2) = 8
The diameter of the circle is 8
Then the radius is:
R = 8/2 = 4
the radius is 4.
Now, to find the center of the circle we just need to go to any of the two extremes of the interval and count 4 units towards the center of the circle, this is:
(-1 + 4, -5) = (3, -5)
or
(7 - 4, -5) = (3, -5)
Then the center of the circle is the point (3, -5) and the radius is R = 4
The equation of the circle is:
(x - 3)^2 + (y - (-5))^2 = 4^2
(x - 3)^2 + (y + 5)^2 = 16