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\vtop{\hsize=3.58in \noindent {\bf Problem statement} A circle with
center on the $y$-axis is tangent to the parabola $y = x^2$ at the
points $(1,1)$ and $(-1,1)$. Find its center and radius. A diagram is
shown to the right.

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\noindent {\it Suggestion:} Find the equation of the normal line to
$\,y = x^2\,$ at the point $(1,1)$, that is, the line that is
perpendicular to the parabola (and circle) at $(1,1)$. How can this be
used to find the circle's center? }

%contributed by Michael O'Nan

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