Chapter 11.7, Problem 5ES

The given equation represent quadric surfaces whose orientations are different from those in Table 11.7.1. In each part, identify the quadric surface, and give a verbal description of its orientation (e.g., an elliptic cone opening along the z-axis or hyperbolic paraboloid straddling the y-axis).

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