The standard equation of a circle with a center $(h, k)$ and radius $r$ is given by:

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

Given the center $(5, -4)$ and radius $3$ units, we can substitute $h = 5$, $k = -4$, and $r = 3$ into the equation.

Substitute the values:

$(x - 5)^2 + (y - (-4))^2 = 3^2$

Simplify the equation:

$(x - 5)^2 + (y + 4)^2 = 9$

Thus, the standard equation of the circle is:

$(x - 5)^2 + (y + 4)^2 = 9$

Would you like more details or have any questions?

Here are 5 related questions that expand on this topic:

1. How would the equation change if the radius was doubled?
2. What is the equation of a circle if its center is at the origin and has the same radius?
3. How do you find the radius of a circle from its equation?
4. Can you explain how to convert this standard form equation into the general form of a circle?
5. How do you determine if a given point lies on the circle using its equation?

Tip: To find the center and radius of a circle from its equation, compare it with the standard form $(x - h)^2 + (y - k)^2 = r^2$ and identify the values of $h$, $k$, and $r$.