Chapter 11.7, Problem 10ES

In these exercises, traces of the surfaces in the planes are conic sections. In each part, find an equation of the trace, and state whether it is an ellipse, a parabola, or a hyperbola.

$\begin{array}{l}\left(\text{a}\right)9x^2-y^2+4z^2=9;x=2\\ \left(\text{b}\right)9x^2-y^2+4z^2=9;y=4\\ \left(\text{c}\right)x^2+4y^2-9z^2=0;y=1\\ \left(\text{d}\right)x^2+4y^2-9z^2=0;z=1\\ \left(\text{e}\right)z=x^2-4y^2;x=1\\ \left(\text{f}\right)z=x^2-4y^2;z=4\end{array}$