MathDB
Today's calculation of Integral 790

Source: 2012 Tokyo University entrance exam/Humanities, problem 4

February 25, 2012
calculusintegrationconicsparabolaanalytic geometrygeometrycalculus computations

Problem Statement

Define a parabola CC by y=x2+1y=x^2+1 on the coordinate plane. Let s, ts,\ t be real numbers with t<0t<0. Denote by l1, l2l_1,\ l_2 the tangent lines drawn from the point (s, t)(s,\ t) to the parabola CC.
(1) Find the equations of the tangents l1, l2l_1,\ l_2.
(2) Let aa be positive real number. Find the pairs of (s, t)(s,\ t) such that the area of the region enclosed by C, l1, l2C,\ l_1,\ l_2 is aa.
Back to ProblemsView on AoPS