You will kick yourself when you realize how easy this was....hehe

Quickly draw out a small grid on paper and plot the point (4,7). The question states that no point on the circle is non-negative. So, the radius cannot extend from the center and pass through either the x-axis or the y-axis.

The center is located 4 units from the y-axis and 7 units from the x-axis. If the radius is 7, then it will extend out beyond the y-axis and give a negative value. If the radius is 4, then it will extend out to the y-axis, but will not cross it. With the radius of 4 it still has 3 units until it hits the x-axis so it is fine.

so, the maximum radius will yield the maximum area...Pi*4^2 = 16Pi

HTH

Aaring23 wrote:Hey guy's I was wondering if someone could help me out with this problem. Here is the problem.

In the XY-Plane, each point on circle K has nonnegative coordinates and the center of K is the point (4,7) What is the maximum possible area of k?

Answer is 16pi.



Any help will be appreciated. Thank you.[/spoiler]

[/quote]

each point on circle K has nonnegative coordinates

This means points should be line in Ist quardrant where both x and y are poitive.

Here points (i.e center points) are (4,7). x=4 and y=7.

circle with radius 4 lies in first quardrant.
cicle with radius 7 lies in I and II qurdrant.

therefore x should be 4.