XY-Plane Question

Aaring23 · Posted: Thu Apr 24, 2008 12:24 pm Post subject: XY-Plane Question

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]

luvaduva · Posted: Thu Apr 24, 2008 7:48 pm Post subject:

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