1. Stating the problem: We have the equation of a circle $$(x + 3)^2 + (y + 5)^2 = 25$$ 2. Find the center and radius: - The equation of a circle in standard form is $$(x - h)^2 + (y - k)^2 = r^2$$ where $$(h, k)$$ is the center and $$r$$ is the radius. - Comparing, we identify $$h = -3$$ (since it is $$x + 3$$, center x-coordinate is $$-3$$) and $$k = -5$$ (center y-coordinate is $$-5$$). - The radius $$r = \sqrt{25} = 5$$. 3. For the graph of circle A: a. The center is given as $$(2, 1)$$. b. The radius is the distance from $$ (2,1) $$ to $$ (2,4) $$, calculated as $$|4 - 1| = 3$$ units. c. The equation of circle A using standard form is: $$ (x - 2)^2 + (y - 1)^2 = 3^2 $$ or $$ (x - 2)^2 + (y - 1)^2 = 9 $$ Final answers: - Circle from given equation: Center $$(-3,-5)$$, Radius $$5$$. - Circle A: Center $$(2,1)$$, Radius $$3$$, Equation $$(x - 2)^2 + (y - 1)^2 = 9$$.