Questions: Find the center-radius form of the equation of the circle described. Then graph the circle. center (sqrt(5), sqrt(6)), radius sqrt(2) Type the center-radius form of the equation of the circle described.

Solution Steps

The center of the circle is given as \((\sqrt{5}, \sqrt{6})\) and the radius is \(\sqrt{2}\).

The center-radius form of a circle's equation is given by: \[ (x - h)^2 + (y - k)^2 = r^2 \] where \((h, k)\) is the center and \(r\) is the radius. Substituting the given values: \[ (x - \sqrt{5})^2 + (y - \sqrt{6})^2 = (\sqrt{2})^2 \]

Simplify the equation by squaring the radius: \[ (x - \sqrt{5})^2 + (y - \sqrt{6})^2 = 2 \]

Final Answer