Precalculus, Chapter 1, 1.4, Section 1.4, Problem 38

Determine the standard form of the equation of a circle with center $(-3,1)$ and tangent to the $y$-axis.

Since the circle is tangent to the $y$-axis, it only touches the y-axis at one point and that is (0,1). Thus, the distance from the center to that point is the absolute value of the $x$-coordinate of the center which happens to be the radius of the circle and that $r=|-3|=3$. Therefore, by using the standard form of the equation of a circle, we obtain...


$
\begin{equation}
\begin{aligned}

\left[x - (-3) \right]^2 + (y-1)^2 =& 3^2
\\
(x + 3)^2 + (y-1)^2 =& 9

\end{aligned}
\end{equation}
$