Question

multiple choice 10 points a circle has the equation ((x + 5)^2 + (y - 2)^2 = 9). what is the center of the circle? ((-5, 2)) ((-5, -2)) ((5, -2)) ((2, -5)) clear my selection previous

Explanation:

Step1: Recall the standard circle equation

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

Step2: Compare with the given equation

The given equation is \((x + 5)^2 + (y - 2)^2 = 9\). Rewrite \(x + 5\) as \(x - (-5)\). So comparing with \((x - h)^2 + (y - k)^2 = r^2\), we have \(h = -5\) and \(k = 2\).

Answer:

\((-5, 2)\)