Write the standard form of the equation of the circle with its center at 

left parenthesis negative 9 comma 0 right parenthesis(−9,0)​, 

and a radius of 

6.

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.

Given that the center is \((-9, 0)\) and the radius is 6, substitute these values into the formula:

\[
(x - (-9))^2 + (y - 0)^2 = 6^2
\]

Simplifying:

\[
(x + 9)^2 + y^2 = 36
\]

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

\[
(x + 9)^2 + y^2 = 36
\]

Would you like further explanation or details?

Here are some related questions:
1. What is the general form of the equation of a circle?
2. How do you find the equation of a circle given a point on the circle?
3. How can you convert the standard form to the general form of a circle equation?
4. How do you find the radius of a circle if only given its equation?
5. What is the process to determine the center of a circle from its equation?

**Tip**: Remember, the terms \((x - h)\) and \((y - k)\) shift the circle's center to \((h, k)\) in the coordinate plane!

Write the standard form of the equation of the circle with its center at (-9, 0), and a radius of 6.

Learn how to write the standard form of the equation of a circle with center at (-9, 0) and radius 6. This problem covers important geometry concepts related to circles and coordinate geometry, suitable for students in Grades 8-10.

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