Problem: The points of intersection of and are joined. The resulting figure is:
Answer Choices:
A. a straight line
B. an equilateral triangle
C. a parallelogram
D. a rectangle
E. a square
Solution:
is a circle with center at the origin. is a hyperbola, symmetric with respect to the line points of intersection are symmetric with respect to . There are either no intersections, two intersections (if the hyperbola is tangent to the circle) or four intersections. Simultaneous solution of the equations reveals that there are four points of intersection, and that they determine a rectangle.