Find the equation of a circle whose center is at (7, -11) and radius is 12 units.

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

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

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

Given:
- Center: \((h, k) = (7, -11)\)
- Radius: \(r = 12\)

Substitute the values into the formula:

\[
(x - 7)^2 + (y + 11)^2 = 12^2
\]

Simplify:

\[
(x - 7)^2 + (y + 11)^2 = 144
\]

Thus, the equation of the circle is:

\[
(x - 7)^2 + (y + 11)^2 = 144
\]

Would you like further details on how this equation represents the circle? 

Here are 5 related questions:
1. How do you derive the equation of a circle from its general form?
2. What is the equation of a circle with a center at the origin and radius 12?
3. How does shifting the center affect the equation of a circle?
4. What would be the equation if the radius of the circle was doubled?
5. How can you determine the center and radius from a given circle equation?

**Tip:** Always ensure the terms in the equation of a circle are in standard form \((x - h)^2 + (y - k)^2 = r^2\) to easily identify the center and radius.

Learn how to find the equation of a circle with center at (7, -11) and radius 12. Understand the standard form equation of a circle and how to substitute center and radius values. Suitable for high school students studying coordinate geometry.

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