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
In the xy plane, each point on the circle k has non negative
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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.)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
Since the maximum radius is 4, the maximum area of circle k is π(4)^2 = 16π.
Answer: C
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Plotting a circle with a radius of 7 will have some of its point on another quadrant which will be a negative x- coordinate.
Since each point on circle K has a non-negative coordinates, the radius of 7 is not possible
Hence, maximum radius possible
$$\le4$$ anything above 4 will be worked out given the non-negative clause.
Maximum possible area of K
= $$\pi r^2$$
Since Maximum possible radius = 4
$$Max\ area=\ \pi\left(4\right)^2=16\pi$$
$$Answer\ is\ Option\ C$$
Since each point on circle K has a non-negative coordinates, the radius of 7 is not possible
Hence, maximum radius possible
$$\le4$$ anything above 4 will be worked out given the non-negative clause.
Maximum possible area of K
= $$\pi r^2$$
Since Maximum possible radius = 4
$$Max\ area=\ \pi\left(4\right)^2=16\pi$$
$$Answer\ is\ Option\ C$$