MathDB

Today's calculation of Integral 121

Source: Kwansei University entrance exam/Literature 1993

July 10, 2006

calculusintegrationconicsparabolaanalytic geometrygeometrycalculus computations

Problem Statement

Given the parabola

C: y=x^{2}.

If the circle centered at

y

axis with radius

1

has common tangent lines with

C

at distinct two points, then find the coordinate of the center of the circle

K

and the area of the figure surrounded by

C

and

K.