1. **State the problem:** Given points $P=(-4,-3)$ and $Q=(2,1)$ as endpoints of the diameter of a circle, find the equation of the circle. 2. **Formula and rules:** The equation of a circle with center $(h,k)$ and radius $r$ is: $$ (x - h)^2 + (y - k)^2 = r^2 $$ The center is the midpoint of the diameter, and the radius is half the length of the diameter. 3. **Find the center $(h,k)$:** $$ h = \frac{x_1 + x_2}{2} = \frac{-4 + 2}{2} = \frac{-2}{2} = -1 $$ $$ k = \frac{y_1 + y_2}{2} = \frac{-3 + 1}{2} = \frac{-2}{2} = -1 $$ So, center is $(-1,-1)$. 4. **Find the radius $r$:** Length of diameter $d$ is distance between $P$ and $Q$: $$ d = \sqrt{(2 - (-4))^2 + (1 - (-3))^2} = \sqrt{6^2 + 4^2} = \sqrt{36 + 16} = \sqrt{52} $$ Radius $r = \frac{d}{2} = \frac{\sqrt{52}}{2} = \sqrt{13}$. 5. **Write the equation:** $$ (x - (-1))^2 + (y - (-1))^2 = (\sqrt{13})^2 $$ Simplify: $$ (x + 1)^2 + (y + 1)^2 = 13 $$ **Final answer:** $$(x + 1)^2 + (y + 1)^2 = 13$$