1. **State the problem:** We have two circles given by their equations: - Circle c: $$(x + 2)^2 + (y - 5)^2 = 36$$ - Circle k: $$(x - 5)^2 + (y + 3)^2 = 25$$ We need to find the centers and radii of both circles and determine the position of the point $(9, 2)$ relative to circle k. 2. **Formula for a circle:** The standard form of a circle's equation is: $$ (x - h)^2 + (y - k)^2 = r^2 $$ where $(h, k)$ is the center and $r$ is the radius. 3. **Find center and radius of circle c:** Given: $$ (x + 2)^2 + (y - 5)^2 = 36 $$ Rewrite as: $$ (x - (-2))^2 + (y - 5)^2 = 6^2 $$ So, center of circle c is $(-2, 5)$ and radius is $6$. 4. **Find center and radius of circle k:** Given: $$ (x - 5)^2 + (y + 3)^2 = 25 $$ Rewrite as: $$ (x - 5)^2 + (y - (-3))^2 = 5^2 $$ So, center of circle k is $(5, -3)$ and radius is $5$. 5. **Determine position of point $(9, 2)$ relative to circle k:** Calculate distance from point to center of k: $$ d = \sqrt{(9 - 5)^2 + (2 - (-3))^2} = \sqrt{4^2 + 5^2} = \sqrt{16 + 25} = \sqrt{41} $$ Since radius of k is $5$, compare $d$ and $r$: - $d = \sqrt{41} \approx 6.4$ - $r = 5$ Because $d > r$, point $(9, 2)$ is **outside** circle k. **Final answers:** - Circle c center: $(-2, 5)$ - Circle c radius: $6$ - Circle k center: $(5, -3)$ - Circle k radius: $5$ - Point $(9, 2)$ is outside circle k.