The equation of a circle in the coordinate plane can be expressed in the standard form:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
From the given information:
- The center of the circle is at \((-4, 6)\), which means \(h = -4\) and \(k = 6\).
- The radius \(r\) is \(2\).
Now, we need to find \(r^2\): \[ r^2 = 2^2 = 4 \]
Substituting these values into the standard equation gives us:
\[ (x - (-4))^2 + (y - 6)^2 = 4 \]
This simplifies to:
\[ (x + 4)^2 + (y - 6)^2 = 4 \]
Now, filling in the missing information in your equation format:
\[ (x - (-4))^2 + (y - 6)^2 = 4 \]
So the final filled-in equation looks like this:
\[ (x + 4)^2 + (y - 6)^2 = 4 \]