Problem:
Two points and are in a plane. Let be the set of all points in the plane for which has area . Which of the following describes ?
Answer Choices:
A. two parallel lines
B. a parabola
C. a circle
D. a line segment
E. two points
Solution:
If the altitude from has length , then has area . The area is if and only if . Thus consists of the two lines that are parallel to line and are units from it, as shown.
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The problems on this page are the property of the MAA's American Mathematics Competitions