Problem:
Which of these describes the graph of
Answer Choices:
A. two parallel lines
B. two intersecting lines
C. three lines that all pass through a common point
D. three lines that do not all pass through a common point
E. a line and a parabola
Solution:
The given equation is equivalent to , which is in turn equivalent to . A product is 0 if and only if one of the factors is 0 , so the graph is the union of the graphs of , and . These are three straight lines, two of which intersect at the origin and the third of which does not pass through the origin. Therefore the graph consists of three lines that do not all pass through a common point.
The problems on this page are the property of the MAA's American Mathematics Competitions