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The problem provides the center of a circle at \( (5, -6) \) and states that the circle is tangent to the y-axis. From this, we can extract the information needed to write the equation of the circle in standard form.

### Step-by-Step Solution:

1. **Standard Form of a Circle**:  
   The equation of a circle in standard form is given by:  
   \[
   (x - h)^2 + (y - k)^2 = r^2
   \]
   where \((h, k)\) is the center of the circle, and \(r\) is the radius.

2. **Center of the Circle**:  
   The center is already provided as \((5, -6)\), so in the equation, \(h = 5\) and \(k = -6\).

3. **Tangent to the y-axis**:  
   Since the circle is tangent to the y-axis, the distance from the center to the y-axis must be equal to the radius of the circle. The distance from the center \((5, -6)\) to the y-axis is 5 units (since the x-coordinate of the center is 5).

   Therefore, the radius of the circle \(r = 5\).

4. **Equation of the Circle**:  
   Now that we know the center and the radius, we can plug these values into the standard form equation:
   \[
   (x - 5)^2 + (y + 6)^2 = 5^2
   \]
   Simplifying:
   \[
   (x - 5)^2 + (y + 6)^2 = 25
   \]

Thus, the equation of the circle in standard form is:
\[
(x - 5)^2 + (y + 6)^2 = 25
\]

Would you like further details or have any questions?

### Related Questions:
1. How do you find the distance between a point and a line in coordinate geometry?
2. How would the equation change if the circle were tangent to the x-axis instead?
3. What is the general formula to calculate the radius of a circle if its center and a point on the circle are known?
4. How would you determine the equation of a circle if it were tangent to both the x-axis and y-axis?
5. Can a circle be tangent to both the x-axis and y-axis, and how would you calculate the radius?

### Tip:
Always remember that the distance from the center of the circle to a tangent line is equal to the radius of the circle.

The center of the circle is (5, -6) and the circle is tangent to the y-axis. Write the equation of the circle in standard form.

Learn how to find the equation of a circle with center (5, -6) that is tangent to the y-axis. This problem demonstrates the application of the standard form of a circle equation, using geometry principles. Suitable for students in Grades 9-11.

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