Chapter 11.7, Problem 2ES

Identify the quadric surface as an ellipsoid, hyperboloid of one sheet, hyperboloid of two sheets, elliptic cone, elliptic paraboloid, or hyperbolic paraboloid by matching the equation with one of the forms given in Table 11.7.1. State the values of a, b, and c in each case.

$\begin{array}{l}\left(\text{a}\right)6x^2+3y^2+4z^2=12\\ \left(\text{b}\right)y^2-x^2-z=0\\ \left(\text{c}\right)9x^2+y^2-9z^2=9\\ \left(\text{d}\right)4x^2+y^2-4z^2=-4\\ \left(\text{e}\right)2z-x^2-4y^2=0\\ \left(\text{f}\right)12z^2-3x^2=4y^2\end{array}$