Question

determine the center and radius of the circle. write your answers as simplified fractions or integers.
$(x - \frac{2}{3})^2+(y + \frac{1}{5})^2=\frac{25}{81}
part: 0 / 2
part 1 of 2
the center is ( , ).

Explanation:

Step1: Recall circle - standard form

The standard form of a circle is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center and $r$ is the radius.

Step2: Identify the center coordinates

For the given equation $(x-\frac{2}{3})^2+(y + \frac{1}{5})^2=\frac{25}{81}$, comparing with the standard - form, we have $h=\frac{2}{3}$ and $k=-\frac{1}{5}$. So the center of the circle is $(\frac{2}{3},-\frac{1}{5})$.

Step3: Calculate the radius

Since $r^2=\frac{25}{81}$, then $r=\sqrt{\frac{25}{81}}=\frac{5}{9}$.

Answer:

Part 1 of 2: The center is $(\frac{2}{3},-\frac{1}{5})$
Part 2 of 2: The radius is $\frac{5}{9}$