Determine the center and radius of the circle. Write your answers as simplified fractions or integers. \[ \left(x+\frac{2}{3}\right)^{2}+\left(y-\frac{6}{7}\right)^{2}=\frac{81}{4} \]

To determine the center and radius of the circle given by the equation: \[ \left(x+\frac{2}{3}\right)^{2}+\left(y-\frac{6}{7}\right)^{2}=\frac{81}{4} \] we can compare it with the standard form of the equation of a circle: \[ (x-h)^2 + (y-k)^2 = r^2 \] where (h, k) is the center of the circle and r is the radius. From the given equation, we can see that: - h = -2/3 - k = 6/7 To find the radius, we take the square root of the right-hand side of the equation: \[ r^2 = \frac{81}{4} \] \[ r = \sqrt{\frac{81}{4}} \] \[ r = \frac{\sqrt{81}}{\sqrt{4}} \] \[ r = \frac{9}{2} \] So, the center of the circle is at \((-2/3, 6/7)\) and the radius is \(9/2\).