Let S 3
​
be the surface with equation given by 4x 2
−9y 2
=9(z 2
+4). 1. Find an equation of the trace of S 3
​
on each of the coordinate planes and on the planes x=±3 2
​
. Determine if each trace is empty, a point, a (pair of) line(s), a parabola, an ellipse, or a hyperbola. 2. What type of quadric surface is S 3
​
? 3. Using the traces obtained in IV.1., provide a hand-drawn sketch of S 3
​
. Label all important points (e.g., vertices) found on each trace. (For graphing purposes, 3 2
​
≈4.2.) 4. View S 3
​
as a surface of revolution. Find an equation of a generating curve on the xy-plane which, if revolved about the x-axis, will result to S 3
​
.