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You didn't think Ellipses would be on AMC 10 ...

Source: 2019 AMC 10B #10/2019 AMC 12B #6

February 14, 2019
conicsellipseAMC 10AMCAMC 10 BAMC 12AMC 12 B

Problem Statement

In a given plane, points AA and BB are 1010 units apart. How many points CC are there in the plane such that the perimeter of △ABC\triangle ABC is 5050 units and the area of △ABC\triangle ABC is 100100 square units?
<spanclass=′latex−bold′>(A)</span>0<spanclass=′latex−bold′>(B)</span>2<spanclass=′latex−bold′>(C)</span>4<spanclass=′latex−bold′>(D)</span>8<spanclass=′latex−bold′>(E)</span>infinitely many<span class='latex-bold'>(A) </span>0\qquad<span class='latex-bold'>(B) </span>2\qquad<span class='latex-bold'>(C) </span>4\qquad<span class='latex-bold'>(D) </span>8\qquad<span class='latex-bold'>(E) </span>\text{infinitely many}
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