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Today's calculation of Integral 870

Source: 2013 Hokkaido University entrance exam, 2nd exam

March 15, 2013
calculusintegrationconicsellipsehyperbolageometryinequalities

Problem Statement

Consider the ellipse E:3x2+y2=3E: 3x^2+y^2=3 and the hyperbola H:xy=34.H: xy=\frac 34.
(1) Find all points of intersection of EE and HH.
(2) Find the area of the region expressed by the system of inequality {3x2+y2≤3emsp;xy≥34,emsp;\left\{ \begin{array}{ll} 3x^2+y^2\leq 3 &  \\ xy\geq \frac 34 , &  \end{array} \right.
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