Write the standard equation of a circle with center (5, -4) and radius 3 units.

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 \(r\).

Learn how to write the standard equation of a circle with center (5, -4) and radius 3 units. This problem involves coordinate geometry and the standard form of a circle equation, (x - h)^2 + (y - k)^2 = r^2. Suitable for high school students.

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