The equation of a circle is generally given by the formula:

$(x - h)^2 + (y - k)^2 = r^2$

Where:

• $(h, k)$ is the center of the circle,
• $r$ is the radius.

In this case, the center of the circle is given as $(-3, 2)$, so $h = -3$ and $k = 2$. Now, since the circle is tangent to the y-axis, the radius is the distance from the center to the y-axis.

The x-coordinate of the center is $-3$, so the distance from the center to the y-axis is simply the absolute value of the x-coordinate, which is:

$r = | -3 | = 3$

Thus, the radius of the circle is $r = 3$.

Substituting $h = -3$, $k = 2$, and $r = 3$ into the standard equation of the circle, we get:

$(x + 3)^2 + (y - 2)^2 = 3^2$

Simplifying:

$(x + 3)^2 + (y - 2)^2 = 9$

Thus, the equation of the circle is:

$(x + 3)^2 + (y - 2)^2 = 9$

---

Would you like further explanation on this or have any additional questions? Here are some related questions you might find helpful:

1. How would you find the equation of a circle with a given center and radius?
2. How can you determine if a circle is tangent to a line or axis?
3. What is the general method for finding the radius of a circle given the center and its tangency point?
4. How can you derive the equation of a circle from a geometric diagram?
5. What happens if the center of the circle is on the x-axis or y-axis?

Tip: Always remember that the radius is the distance from the center to any point on the circle, including points of tangency.