ADVANCED EXERCISES

(2) Given a circle with radius 1 unit and center at (0,0). A rectangle is inscribed inside the circle such that one of its sides is parallel to the x-axis and crosses the y-axis at y. Express the following as functions of x.

 (a) The perimeter of the rectangle

 (b) The area of the rectangle

 (a) Let P = perimeter of rectangle

     P =  2(2x) + 2(2y) = 4x + 4y

     Now 12 = x2 + y2  ==> y = 

     P = 4x + 4


 (b) Area = (2x)(2y)
          = 4xy 
          = 4x