Questions: Write the standard form of the equation of the circle with the given center and radius. Center (-2,2), r=sqrt(3) The equation of the circle in standard form is (Simplify your answer.)

Solution Steps

To write the standard 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 \((-2, 2)\) and radius \(\sqrt{3}\), we can substitute these values into the formula.

The center of the circle is given as \((-2, 2)\) and the radius is \(r = \sqrt{3}\).

The standard form of the equation of a circle is given by: \[ (x - h)^2 + (y - k)^2 = r^2 \] Substituting \(h = -2\), \(k = 2\), and \(r = \sqrt{3}\) into the equation, we have: \[ (x - (-2))^2 + (y - 2)^2 = (\sqrt{3})^2 \]

This simplifies to: \[ (x + 2)^2 + (y - 2)^2 = 3 \]

Final Answer