121

Part of 2006 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 121

Source: Kwansei University entrance exam/Literature 1993

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

K.

calculusintegrationconicsparabolaanalytic geometrygeometrycalculus computations