Problem:
All three vertices of lie on the parabola defined by , with at the origin and parallel to the -axis. The area of the triangle is . What is the length ?
Answer Choices:
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Solution:
Let the vertex of the triangle that lies in the first quadrant be . Then the base of the triangle is and the height is , so . Thus , and .
The problems on this page are the property of the MAA's American Mathematics Competitions