Participation in the Math Q\&A forums is required for Weeks 3 and 4 . Let \( (x+3)^{2}+(y-5)^{2}=121 \). Answer the following questions. a. What does the equation represent? Be specific.

The equation \( (x+3)^{2}+(y-5)^{2}=121 \) represents a circle in the Cartesian coordinate system. To break it down: 1. **Standard Form of a Circle**: The standard form of a circle's equation is given by: \[ (x-h)^{2} + (y-k)^{2} = r^{2} \] where \( (h, k) \) is the center of the circle and \( r \) is the radius. 2. **Identifying Parameters**: - In the given equation, we can identify: - \( h = -3 \) (the x-coordinate of the center) - \( k = 5 \) (the y-coordinate of the center) - \( r^{2} = 121 \), which means \( r = \sqrt{121} = 11 \) (the radius of the circle) 3. **Conclusion**: - The center of the circle is at the point \( (-3, 5) \). - The radius of the circle is \( 11 \). Thus, the equation represents a circle centered at \( (-3, 5) \) with a radius of \( 11 \).