MathDB
Ellipse

Source: AMC 12 2006B, Problem 21

February 17, 2006
conicsellipsegeometryrectangleperimeterAMC

Problem Statement

Rectangle ABCD ABCD has area 2006. An ellipse with area 2006π 2006\pi passes through A A and C C and has foci at B B and D D. What is the perimeter of the rectangle? (The area of an ellipse is πab \pi ab, where 2a 2a and 2b 2b are the lengths of its axes.) <spanclass=′latex−bold′>(A)</span>162006π<spanclass=′latex−bold′>(B)</span>10034<spanclass=′latex−bold′>(C)</span>81003<spanclass=′latex−bold′>(D)</span>62006<spanclass=′latex−bold′>(E)</span>321003π <span class='latex-bold'>(A) </span> \frac {16\sqrt {2006}}{\pi} \qquad <span class='latex-bold'>(B) </span> \frac {1003}4 \qquad <span class='latex-bold'>(C) </span> 8\sqrt {1003} \qquad <span class='latex-bold'>(D) </span> 6\sqrt {2006} \qquad <span class='latex-bold'>(E) </span> \frac {32\sqrt {1003}}\pi
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