Answer: the standard form equation of the circle is:
(x + 5/2)^2 + (y + 1)^2 = 181/4
Step-by-step explanation: In order to find the standard form equation of a circle, we need the center and the radius. First, calculate the midpoint of the diameter, which is the center:
Midpoint = ((-7 - 3) / 2, (-6 + 2) / 2)
Midpoint = (-5/2, -1)
Now, calculate the radius, which is the distance from one of the diameter's endpoints to the center:
Radius = √((-7 - (-5/2))^2 + (-6 - (-1))^2)
Radius = √((-14/2 + 5/2)^2 + (-5)^2)
Radius = √((-9/2)^2 + 25)
Radius = √(81/4 + 25)
Radius = √(181/4)
Now, plug the center and radius into the standard form equation of a circle:
(x - (-5/2))^2 + (y - (-1))^2 = (√(181/4))^2
Simplify:
(x + 5/2)^2 + (y + 1)^2 = 181/4