MathDB

Today's calculation of Integral 771

Source: 1997 Tokyo University entrance exam/Science

January 3, 2012

calculusintegrationconicsparabolageometryanalytic geometrycalculus computations

Problem Statement

(1) Find the range of

a

for which there exist two common tangent lines of the curve

y=\frac{8}{27}x^3

and the parabola

y=(x+a)^2

other than the

x

axis.
(2) For the range of

a

found in the previous question, express the area bounded by the two tangent lines and the parabola

y=(x+a)^2

in terms of

a