Questions: The equation of a circle is given below. Identify the center and radius. The x^2 + y^2 = 4 Center: Radius:

Solution Steps

To identify the center and radius of a circle given its equation, we need to compare the given equation with the standard form of a circle's equation, which is \((x - h)^2 + (y - k)^2 = r^2\). Here, \((h, k)\) is the center of the circle, and \(r\) is the radius. For the given equation \(x^2 + y^2 = 4\), we can see that it is already in the standard form with \(h = 0\), \(k = 0\), and \(r^2 = 4\). Therefore, the center is \((0, 0)\) and the radius is \(\sqrt{4} = 2\).

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.

The given equation is \(x^2 + y^2 = 4\). This can be rewritten in the standard form as \((x - 0)^2 + (y - 0)^2 = 2^2\).

From the comparison, we can see that \(h = 0\) and \(k = 0\), so the center of the circle is \((0, 0)\). The radius \(r\) is determined by taking the square root of 4, which gives \(r = 2\).

Final Answer