Questions: Find the center and radius of the circle. Write the standard The center of the circle is (h, k)=(2,1). (Type an ordered pair.) The radius of the circle is r=

Solution Steps

To find the radius of the circle, we need to use the standard form of the equation of a circle, which is \((x - h)^2 + (y - k)^2 = r^2\). Given the center \((h, k) = (2, 1)\), we need to determine the radius \(r\).

The center of the circle is given as \((h, k) = (2, 1)\).

To find the radius \(r\), we use the distance formula between the center \((h, k)\) and a point on the circle \((x, y)\). Assuming the point \((5, 5)\) lies on the circle, the radius is calculated as: \[ r = \sqrt{(x - h)^2 + (y - k)^2} \] Substituting the values: \[ r = \sqrt{(5 - 2)^2 + (5 - 1)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5.0 \]

Final Answer