Find the equation of the circle with its diameter end points at A(2, -3) and B(-1, 5).

Step 1 ：The center of the circle is the midpoint of the diameter. So, to find the center of the circle, we use the midpoint formula:

Step 2 ：\[ C = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) = \left(\frac{2 + (-1)}{2}, \frac{-3 + 5}{2}\right) = (0.5, 1) \]

Step 3 ：Next, we find the radius of the circle using the distance formula:

Step 4 ：\[ r = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} = \sqrt{(-1-2)^2 + (5-(-3))^2} = \sqrt{9 + 64} = \sqrt{73} \]

Step 5 ：Finally, we can write the equation of the circle using the center-radius form \((x-h)^2 + (y-k)^2 = r^2\), where (h,k) is the center and r is the radius:

Step 6 ：\[ (x - 0.5)^2 + (y - 1)^2 = 73 \]