Questions: Find the center-radius form of the equation of the circle with center (0,0) and radius 11. The center-radius form of the equation of the circle is (Type an equation.)

Solution Steps

To find the center-radius form of the equation of a circle, we use the formula \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center of the circle and \(r\) is the radius. Given the center \((0,0)\) and radius \(11\), we can substitute these values into the formula.

We are given the center of the circle \((h, k) = (0, 0)\) and the radius \(r = 11\).

The center-radius form of the equation of a circle is given by: \[ (x - h)^2 + (y - k)^2 = r^2 \]

Substituting \(h = 0\), \(k = 0\), and \(r = 11\) into the equation, we get: \[ (x - 0)^2 + (y - 0)^2 = 11^2 \]

Simplifying the equation, we obtain: \[ x^2 + y^2 = 121 \]

Final Answer