Problem:
What is the graph of in the coordinate plane?
Answer Choices:
A. two intersecting parabolas
B. two nonintersecting parabolas
C. two intersecting circles
D. a circle and a hyperbola
E. a circle and two parabolas
Solution:
The given equation can be rewritten as . Taking the square root of both sides gives , so either or . The equation in the first case can be rearranged as ; its graph is a hyperbola opening upward and downward. The equation in the second case is equivalent to , whose graph is a circle.
The problems on this page are the property of the MAA's American Mathematics Competitions