\input epsf
\nopagenumbers
\magnification=\magstep1


\noindent {\bf Problem statement} a) Find the value of the positive
constant $C$ so that the parabolas $y = x^2$ and $y = C - x^2$ (shown
in the picture below on the left) intersect at right angles (that is,
the graphs are {\it orthogonal}).

\medskip

\noindent b)) Find the value of the positive constant $D$ so that the
parabolas $y = x^2$ and $y = (D - x)^2$ (shown in the picture below on
the right) intersect at right angles (that is, the graphs are {\it
orthogonal}).

\medskip

\centerline{\epsfxsize=1.5in\epsfbox{nan14a.eps}
\qquad\epsfxsize=1.5in\epsfbox{nan14b.eps}}


%following a problem of  Michael O'Nan

\vfil\eject\end