Problem:
What is the area of the polygon whose vertices are the points of intersection of the curves and ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Solve the first equation for and substitute into the second equation to get , so or . This leads to the intersection points , and . The vertical side of the triangle with these three vertices has length , and the horizontal height to that side has length , so its area is .
The problems on this page are the property of the MAA's American Mathematics Competitions