1. The problem is to understand how to formulate questions involving a circle. 2. A circle is defined by the equation $$ (x - h)^2 + (y - k)^2 = r^2 $$ where $ (h, k) $ is the center and $ r $ is the radius. 3. Common questions about circles include finding the radius, center, area, circumference, or points on the circle. 4. For example, given the equation $$ (x - 3)^2 + (y + 2)^2 = 16 $$, you can ask: - What is the center of the circle? - What is the radius? - What is the circumference? - What is the area? 5. To find the center, identify $h$ and $k$ from the equation: center is $(3, -2)$. 6. The radius $r$ is the square root of 16, so $r = 4$. 7. Circumference is calculated by the formula $$ C = 2\pi r $$, so $$ C = 2\pi \times 4 = 8\pi $$. 8. Area is calculated by $$ A = \pi r^2 $$, so $$ A = \pi \times 4^2 = 16\pi $$. 9. These steps show how to create and solve questions about circles using their standard equation.