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To write the standard form of the equation of a circle, we use the formula:

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

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

In this case, the center is \((-3, 6)\) and the radius \(r = 7\).

Substitute these values into the formula:

\[
(x - (-3))^2 + (y - 6)^2 = 7^2
\]

Simplifying:

\[
(x + 3)^2 + (y - 6)^2 = 49
\]

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

\[
(x + 3)^2 + (y - 6)^2 = 49
\]

Would you like further details or have any questions?

Here are 5 related questions to further explore the concept:
1. How do you find the center and radius of a circle given its equation in standard form?
2. What is the general form of a circle's equation, and how can you convert the standard form to it?
3. If the radius is doubled, how does the equation change?
4. How do you derive the equation of a circle from its diameter endpoints?
5. How do you graph a circle given its standard form equation?

**Tip:** The square of the radius \(r^2\) is always positive, and even if the center coordinates have negative values, the form keeps them clearly as \((x - h)\) and \((y - k)\).

Write the standard form of the equation of a circle with center (-3, 6) and radius r = 7.

Learn how to write the standard form of the equation of a circle with center (-3, 6) and radius r = 7. This solution provides a step-by-step explanation, covering key geometry concepts like circle equations and coordinate geometry. Suitable for students in Grades 9-10.

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