In the xy plane, each point on the circle k has non negative

BTGmoderatorLU wrote:Source: GMAT Prep

In the xy plane, each point on the circle k has non-negative coordinates and the center of k is the point (4, 7). What is the max possible area of k?
$$A.\ 4\pi$$
$$B.\ 9\pi$$
$$C.\ 16\pi$$
$$D.\ 28\pi$$
$$E.\ 49\pi$$
The OA is C

If the center of circle k is (4, 7) and all the points on the circle have non-negative coordinates, then the maximum length of the radius is 4. Assume that we draw the radius 4 units to the left the center, then, it will intersect the y-axis at (0, 7). In other words, this circle has a point (0, 7) on its circumference, while all the other points will have positive coordinates. (If we draw the radius any longer, we will have points containing negative values.)

Since the maximum radius is 4, the maximum area of circle k is π(4)^2 = 16π.

Answer: C