MathDB
Today's calculation of Integral 756

Source: 2011 Tohoku University entrance exam

September 13, 2011
calculusintegrationgeometryanalytic geometrycalculus computations

Problem Statement

Let aa be real number. A circle CC touches the line y=−xy=-x at the point (a,−a)(a, -a) and passes through the point (0, 1).(0,\ 1). Denote by PP the center of CC. When aa moves, find the area of the figure enclosed by the locus of PP and the line y=1y=1.
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