Questions: Find the center and the radius of the circle. Then graph the circle. x^2 + y^2 = 49 The center is (Simplify your answer. Type an ordered pair.)

Solution Steps

The given equation is: \[ x^{2} + y^{2} = 49 \]

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. Comparing this with the given equation, we see that \(h = 0\) and \(k = 0\).

The right side of the equation is \(49\), which is \(r^{2}\). Therefore, the radius \(r\) is: \[ r = \sqrt{49} = 7 \]

Final Answer