hey, can someone help? a rectangle is inscribed in a circle of radius 2. Let P=(x,y) be the point in quadrant I that is a vertex of the rectangle and is on the circle. express the area A of the rectangle as a function of x.

Question

hey, can someone help?  a rectangle is inscribed in a circle of radius 2.  Let P=(x,y) be the point in quadrant I that is a vertex of the rectangle and is on the circle.  express the area A of the rectangle as a function of x.

anonymous · Answer

If the center of the circle is located on the origin then:
One side of the rectangle would be 2x and the other side square root(16-4x^2).
Area=2x*sqrt(16-4x^2)/2
if the center of the circle is not located on the origin but on (cx,cy) then: Area=2(x-cx)*sqrt(16-4(x-cx)^2)/2