Answer
$(x - 2)^2 + (y - 3)^2 = 9$
Work Step by Step
First, we need to find the radius of the circle, so we need to see how far from the center the point given lies. We know that the circle touches the $x-axis$ (because the circle is tangent to the $x$-axis), meaning that the $y$ value of the center would actually be the radius. So, the radius is $3$:
$r = \sqrt {(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Now, we can plug in the center and the radius into the standard equation for a circle, which is given by the formula:
$(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center of the circle, and $r$ is the radius.
Let us plug in our values:
$(x - 2)^2 + (y - 3)^2 = 3^2$
Evaluate the exponent:
$(x - 2)^2 + (y - 3)^2 = 9$
