Questions: Write the standard form of the equation of the circle with the given center and radius. Center (6,-2), r=sqrt(6) The equation of the circle in standard form is (x-6)^2+(y+2)^2=

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 \((6, -2)\) and radius \(\sqrt{6}\), we can substitute these values into the formula.

Given the center \((6, -2)\) and radius \(r = \sqrt{6}\).

The standard form of the equation of a circle is: \[ (x - h)^2 + (y - k)^2 = r^2 \] Substitute \(h = 6\), \(k = -2\), and \(r = \sqrt{6}\): \[ (x - 6)^2 + (y - (-2))^2 = (\sqrt{6})^2 \]

Simplify the equation: \[ (x - 6)^2 + (y + 2)^2 = 6 \]

Final Answer