The circle that has a center of $(-3,4)$ and is tangent to the $y$-axis is graphed in the standard $(x,y)$ coordinate plane below. What is the area, in square coordinate units, of this circle?

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Since the circle is tangent to the $y$-axis, the horizontal distance from the center of the circle to the $y$-axis is 3.

$$A= \pi r^2$$ $$A = \pi (3)^2$$ $$=\boxed{9\pi}$$