The rectangle shown in the figure is inscribed in a semicircle 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. As the point (𝑥,𝑦) on the circle changes, a variety of rectangles are obtained.
I don't mind helping to find answers, but I resent having to provide the questions as well.
I assume you want to find the maximum area.
Assuming the center of the circle is at (0,0) you have
A = 2xy = 2x√(4-x^2)
now find where dA/dx = 0