Find the standard form of the equation for the circle with the following properties.
Center $\left(9, \frac{7}{4}\right)$ and tangent to the $y$-axis

Step 1 ：The standard form of the equation for a circle is \((x-h)^2 + (y-k)^2 = r^2\), where \((h, k)\) is the center of the circle and \(r\) is the radius.

Step 2 ：Given that the circle is tangent to the y-axis, the radius of the circle is equal to the x-coordinate of the center. Therefore, the radius is 9.

Step 3 ：Substitute the center \((9, \frac{7}{4})\) and the radius 9 into the standard form of the equation for a circle to get the equation of the circle.

Step 4 ：The final equation is \((x-9)^2 + (y-\frac{7}{4})^2 = 9^2\).

Step 5 ：Final Answer: The standard form of the equation for the circle is \(\boxed{(x-9)^2 + (y-\frac{7}{4})^2 = 81}\).