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

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

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Source: GMAT Paper Tests

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. 4pi
B. 9pi
C. 16pi
D. 28pi
E. 49pi

The OA is C

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BTGmoderatorLU wrote:
Source: GMAT Paper Tests

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. 4pi
B. 9pi
C. 16pi
D. 28pi
E. 49pi

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. Assuming that we draw the radius 4 units to the left of the circle’s 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 on the circumference will have positive coordinates. (If we were to draw the radius any longer, we would have points on the circle’s circumference containing negative x-coordinates.)

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

Answer: C

_________________
Scott Woodbury-Stewart Founder and CEO

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Plotting a circle with radius 7 will have some of its points on another quadrant which will be a negative x- coordinates.
Since each point on circle K has non-negative coordinates, the radius of 7 is not possible, hence
$$\max\ possible\ radius\le4\ $$
Anything above 4 will not workout given the non-negative clauses
$$\max\ possible\ area\ of\ K=\pi r^2\ $$
since maximum radius = 4
$$\max\ Area=\pi\left(4\right)^2=16\pi$$
$$answer\ is\ Option\ C$$

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