The first step is to find the center of the circle. The center (h, k) is the midpoint of the diameter. To find this, use the midpoint formula, which is the average of the x values (x1 + x2 / 2) and the average of the y values (y1 + y2 / 2).
Substitute the given points into the formula:
h = (-2 + -6) / 2 = -4
k = (3 + -6) / 2 = -1.5
So, the center of the circle is (-4, -1.5).
The next step is to find the radius of the circle. This can be found by using the distance formula, which is the square root of the sum of the squares of the differences between the x and y coordinates divided by 2.
Substitute the given points into the formula:
r = sqrt(((-2 - (-6))^2 + (3 - (-6))^2) / 2) = 4.924428900898052
So, the radius of the circle is approximately 4.924.
Having known the center (h, k) and the radius r of the circle, we can now form the equation of the circle using the standard form:
(x - h)^2 + (y - k)^2 = r^2
Substitute the found values into the standard form:
(x - (-4))^2 + (y - (-1.5))^2 = (4.924)^2
Therefore, the equation of the circle is:
(x + 4)^2 + (y + 1.5)^2 = 4.924^2