Find the equation of a circle whose center is (-4, 11) and radius is √5 units.

To find the equation of a circle given its center and radius, you can use the standard form of the circle equation:

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

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

Given the center of the circle is \((-4, 11)\) and the radius is \(\sqrt{5}\), we can substitute these values into the equation:

\[
h = -4, \quad k = 11, \quad r = \sqrt{5}
\]

Substituting into the standard form, we get:

\[
(x - (-4))^2 + (y - 11)^2 = (\sqrt{5})^2
\]

This simplifies to:

\[
(x + 4)^2 + (y - 11)^2 = 5
\]

So, the equation of the circle is:

\[
\boxed{(x + 4)^2 + (y - 11)^2 = 5}
\]

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### Related Questions:

1. How do you find the radius of a circle if you are given the equation of the circle?
2. How do you find the center of a circle given its equation?
3. What is the general form of the equation of a circle, and how does it relate to the standard form?
4. How do you determine the intersection points of two circles?
5. How can you find the equation of a tangent line to a circle at a given point?

### Tip:

To quickly identify the center and radius of a circle from its standard form equation, look for the expressions \((x-h)^2\) and \((y-k)^2\), which reveal the coordinates \((h, k)\), and equate the right-hand side to \(r^2\) to find the radius \(r\).

Learn how to find the equation of a circle given its center at (-4, 11) and radius √5 with a detailed step-by-step solution. This problem covers key geometric concepts, including the standard form of the circle equation. Suitable for students in Grades 9-12.

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