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