Questions: The equation of a circle is given below. Identify the center and radius. Then graph the circle (x+5)^2+(y+2)^2=16 Center: Radius:

Solution Steps

The equation of the circle is given in the standard form \((x + 5)^2 + (y + 2)^2 = 16\). The standard form of a circle's equation is \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center of the circle and \(r\) is the radius.

In this equation, \((x + 5)^2 + (y + 2)^2 = 16\), we can rewrite it as \((x - (-5))^2 + (y - (-2))^2 = 16\). Therefore, the center \((h, k)\) is \((-5, -2)\).

The radius \(r\) is found by taking the square root of the right-hand side of the equation. Here, the right-hand side is 16, so \(r = \sqrt{16} = 4\).

To graph the circle, plot the center at \((-5, -2)\) on the coordinate plane. Then, draw a circle with a radius of 4 units around this center.

Final Answer