Given a circle with a center at point A(-1, 3) and another point on the circle B(1, 1), find the equation of the circle.

Step 1 ：Step 1: Find the radius of the circle. The radius is the distance between the center of the circle and any point on the circle. We can use the distance formula to find the radius: \(r = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

Step 2 ：Substitute the coordinates of points A and B into the formula: \(r = \sqrt{(1-(-1))^2 + (1-3)^2} = \sqrt{4 + 4} = \sqrt{8}\)

Step 3 ：Step 2: Substitute the center of the circle (h, k) and the radius r into the equation of a circle: \((x-h)^2 + (y-k)^2 = r^2\)

Step 4 ：Substitute h = -1, k = 3 and r = \sqrt{8} into the formula: \((x-(-1))^2 + (y-3)^2 = (\sqrt{8})^2\)

Step 5 ：Simplify the equation to get the final equation of the circle: \((x+1)^2 + (y-3)^2 = 8\)