the edges of the diameter of a circle are at (−1,2) and (3,−1). write the equation of the circle in general form. show all of your work.

(x - 1)^2 + (y - 0.5)^2 = 25.

Step-by-step explanation:

We need to calculate the radius and the coordinates of the center of the circle.

The center is at the midpoint of the diameter =  (-1 + 3)/2 ,  (2+-1)/2

= (1, 0.5).

The radius = 1/2 * diameter = 1/2 * √[ (-1-3)^2 + (2 - -1)^2 ]

r = √25/2 = 2.5

r^2 =  2.5^2 = 6.25.

The general form of the equation is

(x - a)^2 + (y -b)^2 = r^2   where (a,b) is the center and r = the radius.

So the required equation is:

(x - 1)^2 + (y - 0.5)^2 = 6.25.