1. **Problem:** Plot the circle with center coordinates (5,4) and radius 2 units. 2. **Formula:** The equation of a circle with center $(h,k)$ and radius $r$ is given by: $$ (x - h)^2 + (y - k)^2 = r^2 $$ 3. **Apply values:** Here, $h=5$, $k=4$, and $r=2$. Substitute these into the formula: $$ (x - 5)^2 + (y - 4)^2 = 2^2 $$ 4. **Simplify:** $$ (x - 5)^2 + (y - 4)^2 = 4 $$ 5. **Explanation:** This equation represents all points $(x,y)$ that are exactly 2 units away from the center point $(5,4)$. 6. **Final answer:** The equation of the circle is: $$ (x - 5)^2 + (y - 4)^2 = 4 $$