A circle of radius r is centered at the origin and a rectangle is inscribed. The area of the rectangle as a function is given by what? Can you also explain the processes behind finding the answer it helps me understand.

Answer 1

Let the rectangle have a base length of 2x and a height of 2y.
The the 4 vertices of the rectangle are:
(x,y) in I, (-x,y) in II, (-x,-y) in III and (x,-y) in quadrant IV
the area of the rectangle is 4xy but
x^2 + y^2 = r^2 , where r is the radius
from which y = √(r^2 - x^2)

Area of rectangle = 4x√(r^2 -x^2)