Consider the following equation of a circle.
\[
\left(x-\frac{7}{9}\right)^{2}+\left(y+\frac{1}{4}\right)^{2}=\frac{49}{4}
\]

Step 3 of 3 : Find three points that lie on the circle.

Step 1 ：Consider the equation of a circle \(\left(x-\frac{7}{9}\right)^{2}+\left(y+\frac{1}{4}\right)^{2}=\frac{49}{4}\).

Step 2 ：The equation of the circle is given in the standard form \((x-h)^2 + (y-k)^2 = r^2\), where \((h, k)\) is the center of the circle and \(r\) is the radius.

Step 3 ：To find points on the circle, we can choose values for \(x\) and solve for \(y\), or vice versa. We can choose simple values for \(x\) such as \(h-r\), \(h\), and \(h+r\), which correspond to the leftmost, center, and rightmost points on the circle, respectively.

Step 4 ：Let's calculate the points. The center of the circle is \(h = 0.778\) and the radius is \(r = 3.5\).

Step 5 ：By substituting these values into the equation, we get the points \((-2.722, -0.250)\), \((0.778, -3.750)\), and \((4.278, -0.250)\).

Step 6 ：Final Answer: The three points that lie on the circle are \(\boxed{(-2.722, -0.250)}\), \(\boxed{(0.778, -3.750)}\), and \(\boxed{(4.278, -0.250)}\).