Write the standard form of the equation of the circle with the given characteristics. Center: (6,-4) and Radius: 	17

The standard form of the equation of a circle is given by:

\[
(x - h)^2 + (y - k)^2 = r^2
\]

Where:
- \((h, k)\) is the center of the circle.
- \(r\) is the radius of the circle.

Given:
- Center: \((6, -4)\)
- Radius: \(17\)

Substituting the values into the standard form:

\[
(x - 6)^2 + (y + 4)^2 = 17^2
\]

Simplifying \(17^2\):

\[
(x - 6)^2 + (y + 4)^2 = 289
\]

So, the standard form of the equation of the circle is:

\[
(x - 6)^2 + (y + 4)^2 = 289
\]

Would you like details or have any questions? 

Here are 5 related questions:

1. How do you convert the standard form of a circle's equation to the general form?
2. What is the center-radius form of the equation for a circle centered at the origin?
3. How do you find the radius of a circle given the equation in standard form?
4. Can the radius of a circle be negative? Why or why not?
5. How do you determine the diameter of a circle if you know the radius?

**Tip:** Remember, the radius squared \(r^2\) in the equation is always positive, ensuring that the circle has a real radius.

Learn how to write the standard form of the equation of a circle with center (6,-4) and radius 17. This problem involves applying the standard equation of a circle, understanding circle properties, and practicing coordinate geometry. Suitable for high school students.

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