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\begin{document}
\hspace{1in}\Huge{Planes in 3D}
\vskip .1 in
\normalsize


\begin{enumerate}
\item Sketch the plane $3x-2y+2z=6$.

 \vspace{-4in}\hspace{1.3in}\includegraphics[height=8.5in]{3Daxis}

\vspace{-4in}\item Where does the line $x=y-1=2z$ \\
intersect the plane $3x-2y+2z=6$?
\vskip 1.5in
\item Consider the planes $3x-2y+z=1$ and $2x+y-3z=3$\\
\begin{enumerate}
\item Find the angle between the two planes.
\vfill
\item Find the line of intersection between the two planes.
\vfill
\end{enumerate}

\item Find the distance from the origin to the plane $3x-2y+2z=6$.
\vfill
%\item Find the distance between the planes $2x-y+z=1$ and $6x-3y+3z=1$.
%\vfill

\end{enumerate}

\newpage
\begin{center}
\Huge{\S10.5 Conic Sections}
\end{center}
\vskip .1 in

\begin{itemize}
\item The equation of a {\it parabola} with focus $(0,p)$ and directrix $y=-p$ is $$x^2 = 4py.$$
The equation of a parabola with focus $(p,0)$ and directrix $x=-p$ is
$$y^2 = 4px.$$


\item The ellipse $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \qquad a \geq b > 0$$
has foci $(\pm (a^2-b^2), 0)$ and vertices $(\pm a, 0)$, $(\pm b, 0)$.

\item The hyperbola $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1, \qquad a \geq b > 0$$
has foci $(\pm (a^2+b^2), 0)$ and vertices $(\pm a, 0)$ and asymptotes $y=\pm(b/a)x$.
\end{itemize}

\begin{center}
\Huge{3D Conic Sections}
\end{center}
\vskip .1 in

\noindent Match each function to its graph

$9x^2 + 36y^2 + 4z^2 = 36$ \hspace{1in} $4 x^2 + 9y^2 -4z^2 =0$ \hspace{1in}$36 x^2 + 9 y^2 -4z^2 = 36$


 \includegraphics[bb=0 1 238 286,width=2in,height=2.39in,keepaspectratio]{3d-cone.png}     
  \includegraphics[bb=0 1 238 276,width=2in,height=2.31in,keepaspectratio]{3d-hyperboloid-onesheet.png}
 \includegraphics[bb=0 1 238 276,width=2in,height=2.31in,keepaspectratio]{3d-ellipsoid.png}

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