A circle is drawn on a coordinate plane with the center point at (−4,6) and a radius of 2. Derive the equation of the circle from the given information. Fill in the missing information in the following equation.
The general equation for a circle with center at (h,k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center is (-4,6) and the radius is 2. Plugging this information into the general equation, we get:
(x - (-4))^2 + (y - 6)^2 = 2^2
(x + 4)^2 + (y - 6)^2 = 4
Therefore, the equation of the circle is:
(x + 4)^2 + (y - 6)^2 = 4