https://file.aiquickdraw.com/mathbot/file/1723143099271l5o74ce7.pdf

. Find the equation of circle with the coordinates (-2, 3) and radius 6. Using the formula from the file

To find the equation of a circle, we can use the standard form equation:

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

where \((h, k)\) is the center of the circle and \(r\) is the radius.

Given:
- Center \((h, k) = (-2, 3)\)
- Radius \(r = 6\)

Substituting these values into the formula:

\[
(x - (-2))^2 + (y - 3)^2 = 6^2
\]

Simplifying:

\[
(x + 2)^2 + (y - 3)^2 = 36
\]

Thus, the equation of the circle is:

\[
(x + 2)^2 + (y - 3)^2 = 36
\]

Would you like more details or have any questions? 

Here are 8 related questions:
1. How do you find the center and radius from a given circle equation?
2. What is the general form of a circle's equation?
3. How do you convert the standard form of a circle's equation to the general form?
4. How would the equation change if the circle was centered at the origin?
5. What is the significance of the coefficients in the general form of a circle's equation?
6. Can a circle's equation be represented in polar coordinates?
7. How would you determine if a point lies on, inside, or outside the circle?
8. How do you find the equation of a tangent to a circle at a given point?

**Tip:** When dealing with the circle's equation, ensure you correctly identify the center and radius before substituting them into the formula.

Learn how to find the equation of a circle given its center at (-2, 3) and radius of 6 units. Detailed step-by-step solution using the standard form equation of a circle. Suitable for high school students.

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