In the standard (x,y) coordinate plane, the graph of (x – 2)^{2} + (y + 4)^{2} = 9 is a circle. What is the area enclosed by this circle, expressed in square coordinate units?

A. A circle with area 3 has radius , since ()^{2} = 3; but the radius of the given circle is 3, not .

Incorrect

B. A circle with area 4 has radius 2, since (2)^{2} = 4; but the radius of the given circle is 3, not 2.

Incorrect

C. A circle with area 6 has radius , since ()^{2} = 6; but the radius of the given circle is 3, not .

Correct!

The correct answer is D.
Since circles have equations of the form (x – h)^{2} + (y – k)^{2} = r^{2}, for the given circle, r^{2} = 9, so r = 3. Then A = r^{2} = (3)^{2} = 9.

Incorrect

E. A circle with area 16 has radius 4, since (4)^{2} = 16; but the radius of the given circle is 3, not 4.