Answer:
(x + 5)^2 + (y - 4)^2 = 2^2
Step-by-step explanation:
The standard form of the equation of a circle of center (h, k) and radius r
is (x - h)^2 + (y - k)^2 = r^2.
Here the tangent line is y = 2. This is a horizontal line. The point of tangency has the same x-coordinate as does the center (-5, 4); that is, this point is (-5, 2). These two facts tell us that the radius of the circle is (4 - 2), or 2.
Filling in the knowns h = -5, k = 2 and r = 2, we get the equation of this circle:
(x + 5)^2 + (y - 4)^2 = 2^2
