Questions: Give the center and radius of the circle described by the equation and graph the equation. Use the graph to identify the domain and range. (x+2)^2+(y+6)^2=25

Solution Steps

The given equation of the circle is: \[ (x+2)^{2}+(y+6)^{2}=25 \] This is in the standard form \((x-h)^2 + (y-k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius.

From the equation \((x+2)^2 + (y+6)^2 = 25\), we can see that \(h = -2\) and \(k = -6\). Therefore, the center of the circle is: \[ (-2, -6) \]

The radius \(r\) is the square root of 25: \[ r = \sqrt{25} = 5 \]

Final Answer