1. **State the problem:** We are given the equation of a circle in standard form: $$ (x + \frac{5}{7})^2 + (y + \frac{7}{4})^2 = \frac{64}{81} $$ We need to find the center and radius of this circle. 2. **Recall the standard form of a circle's equation:** $$ (x - h)^2 + (y - k)^2 = r^2 $$ where $(h, k)$ is the center and $r$ is the radius. 3. **Identify the center:** In the given equation, the terms are $(x + \frac{5}{7})^2$ and $(y + \frac{7}{4})^2$. Rewrite as: $$ (x - (-\frac{5}{7}))^2 + (y - (-\frac{7}{4}))^2 = \frac{64}{81} $$ So the center is: $$ \left(-\frac{5}{7}, -\frac{7}{4}\right) $$ 4. **Find the radius:** The right side of the equation is $r^2 = \frac{64}{81}$. Take the square root: $$ r = \sqrt{\frac{64}{81}} = \frac{\sqrt{64}}{\sqrt{81}} = \frac{8}{9} $$ 5. **Final answer:** The center is $\left(-\frac{5}{7}, -\frac{7}{4}\right)$ and the radius is $\frac{8}{9}$.