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\noindent {\bf Problem statement} 
The parametric curve $\cases{x =\sqrt{3}\sin t +{1\over 2}\cos t\cr
y=-\sin t+{\sqrt{3}\over 2}\cos t\cr}$ is a tilted ellipse whose graph
is shown to the right. What are the dimensions and location of the box
containing the ellipse?

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\noindent {\bf Note} The sides of the box are vertical and horizontal
and also are tangent to the ellipse.

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