Question

A circle is drawn on a coordinate plane with the center point at (-4, 6) and a radius of 2. Fill in the missing information to find the equation of the circle.(3 points)
(x -
)2 + (y -
)2=

Answer 1

The general equation of a circle with center \((h, k)\) and radius \(r\) is given by:

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

In your case, the center of the circle is at \((-4, 6)\) (\(h = -4\) and \(k = 6\)) and the radius is \(2\) (\(r = 2\)).

First, we need to calculate \(r^2\):

\[
r^2 = 2^2 = 4
\]

Now we can fill in the missing information in the equation format:

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

This simplifies to:

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

So the final equation of the circle is:

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

Thus, the filled information is:

- \(h = -4\)
- \(k = 6\)
- \(r^2 = 4\)

So the equation can be expressed as:

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

or simply

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