\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Two curves intersect orthogonally
when their tangent lines at each point of intersection are
perpendicular. Suppose $C$ is a positive number. The curves $y=Cx^2$
and $y={1\over{x^2}}$ intersect twice. Find $C$ so that the curves
intersect orthogonally. For that value of $C$, sketch both curves when
$-2\le x\le 2$ and $0\le y\le 4$.




\vfil\eject\end