Question

A rectangle is inscribed in a circle of radius 4 centered around the origin. Write a function A(x) for the area of the rectangle.

==> I have no idea how to do this. Can someone help me please? Thanks!!

Answer 1

The circle has a radius of r=4, centred around the origin. Therefore any point (x,y) on the circumference can be obtained by the relation
r²=x²+y².......(1)
by the Pythagorean theorem.
The four corners of the rectangle have to lie on the circumference of the circle.
In fact, if one corner is x,y (in the first quadrant, therefore x≥0, y≥0), the the other points are (-x,y), (x,-y) and (-x,-y).
The width and breath are therefore
2x and 2y, and the area, A(x,y)=2x*2y=4xy........(2)
Using equation (1) above, it is possible to express y in terms of x and r.
Substitute and eliminate y from equation (2) to get:
A(x) = 4x.(..y...)

Can you take it from here?