To express the equation of a circle in standard form, the general formula is:

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

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

Given:
- Center: \(C(-4, 6)\)
- Radius: \(r = 5\)

Substitute these values into the formula:

\[
(x - (-4))^2 + (y - 6)^2 = 5^2
\]

Simplify:

\[
(x + 4)^2 + (y - 6)^2 = 25
\]

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

\[
(x + 4)^2 + (y - 6)^2 = 25
\]

Would you like more details on the steps? Here are 5 related questions:

1. How do you find the equation of a circle if the diameter is given instead of the radius?
2. What is the general form of a circle’s equation, and how is it related to the standard form?
3. How can you find the radius if the equation is given in standard form?
4. How do you convert the equation of a circle from general to standard form?
5. What is the significance of the center and radius in real-world applications?

**Tip:** The square of the radius \(r^2\) helps simplify distance calculations in geometry.

Learn how to find the standard form of a circle's equation with a center at (-4,6) and a radius of 5. This step-by-step guide covers the formula (x - h)^2 + (y - k)^2 = r^2 and simplifies it to (x + 4)^2 + (y - 6)^2 = 25. Suitable for Grades 9-10 geometry students.

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