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Kite Formed by Intersections of Parabolas with Axes

Source: 2015 AMC 12A #12

February 4, 2015
conicsparabolaanalytic geometrygeometryAMC 10AMC

Problem Statement

The parabolas y=ax2−2y=ax^2-2 and y=4−bx2y=4-bx^2 intersect the coordinate axes in exactly four points, and these four points are the vertices of a kite of area 1212. What is a+ba+b?
<spanclass=′latex−bold′>(A)</span>1<spanclass=′latex−bold′>(B)</span>1.5<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>2.5<spanclass=′latex−bold′>(E)</span>3<span class='latex-bold'>(A) </span>1\qquad<span class='latex-bold'>(B) </span>1.5\qquad<span class='latex-bold'>(C) </span>2\qquad<span class='latex-bold'>(D) </span>2.5\qquad<span class='latex-bold'>(E) </span>3
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