For this activity, we will be looking at a variety properties that will help us draw a graph of the surface described by \(\frac{x^2}{4}+\frac{y^2}{9}-\frac{z^2}{1}=1\text{.}\)
Find an equation for the curve given by the intersection of \(\frac{x^2}{4}+\frac{y^2}{9}-\frac{z^2}{1}=1\) with the \(xy\)-plane, the \(yz\)-plane, and the \(xz\)-plane. Draw a two-dimensional plot of each intersection.
Find equations for the curve given by the intersection of \(\frac{x^2}{4}+\frac{y^2}{9}-\frac{z^2}{1}=1\) with the each of the following fundamental planes. You should state the shape and any other characteristics (like center or direction) for each of these intersections.
Which of the following surface plots will correspond to \(\frac{x^2}{4}+\frac{y^2}{9}-\frac{z^2}{1}=1\text{?}\) You can determine this by comparing the features on your previous part to these options.
