The center of a circle is at (–5, 2) and the diameter is 16 units. What is the equation of the circle?

Answer 1

The equation of a circle with center (h, k) and radius r is (x - h)^2 + (y - k)^2 = r^2.

In this case, the center is (-5, 2) and the radius (which is half of the diameter) is 8 units.

Therefore, the equation of the circle would be:
(x - (-5))^2 + (y - 2)^2 = 8^2
(x + 5)^2 + (y - 2)^2 = 64

So, the equation of the circle is (x + 5)^2 + (y - 2)^2 = 64.