9. What is the perimeter of a square that is inscribed in a circle with circ 10. Two men are repainting a wall. Working alone, the first man can fini man in 12 hours. Working together, what part of the wall can they rep 11. What is the center of the circle with equation \( x^{2}+y^{2}-4 y=10 \) ?

To find the center of the circle given by the equation: \[ x^{2} + y^{2} - 4y = 10 \] **Step 1: Rewrite the Equation** Start by rearranging the equation to group the \( y \)-terms: \[ x^{2} + y^{2} - 4y = 10 \] **Step 2: Complete the Square for the \( y \)-Terms** To complete the square for the \( y \)-terms: 1. Take the coefficient of \( y \), which is \(-4\), divide it by 2, and square it: \[ \left(\frac{-4}{2}\right)^2 = (-2)^2 = 4 \] 2. Add and subtract this value within the equation to maintain equality: \[ x^{2} + (y^{2} - 4y + 4) - 4 = 10 \] 3. Simplify the equation: \[ x^{2} + (y - 2)^2 - 4 = 10 \] **Step 3: Isolate the Perfect Square** Move the constant term to the right side of the equation: \[ x^{2} + (y - 2)^2 = 14 \] **Step 4: Identify the Center** The equation now resembles the standard form of a circle: \[ (x - h)^2 + (y - k)^2 = r^2 \] Where \((h, k)\) is the center and \( r \) is the radius. Comparing: \[ (x - 0)^2 + (y - 2)^2 = 14 \] **Conclusion:** The center of the circle is at the point \((0, 2)\). **Answer:** The center of the circle is at the point \( (0,\; 2) \).