Questions: Chapter 2 Test Question 9 of 30 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+5)^2+(y+6)^2=9 The center is (Type an ordered pair. Simplify your answer.) The radius is (Type an integer or a simplified fraction.) Graph the circle. Express the domain of the relation in interval notation. Express the range of the relation in interval notation.

Solution Steps

The equation of the circle is given by: \[ (x+5)^{2}+(y+6)^{2}=9 \] This is in the standard form \((x-h)^2 + (y-k)^2 = r^2\), where \((h, k)\) is the center of the circle. Comparing, we find: \[ h = -5, \quad k = -6 \] Thus, the center of the circle is \((-5, -6)\).

The radius \(r\) is given by the square root of the right-hand side of the equation: \[ r = \sqrt{9} = 3 \] Thus, the radius of the circle is \(3\).

The domain of the circle is determined by the horizontal extent of the circle. Since the center is at \((-5, -6)\) and the radius is \(3\), the domain is: \[ [-5 - 3, -5 + 3] = [-8, -2] \]

The range of the circle is determined by the vertical extent of the circle. Since the center is at \((-5, -6)\) and the radius is \(3\), the range is: \[ [-6 - 3, -6 + 3] = [-9, -3] \]

Final Answer