## Thomas' Calculus 13th Edition

Rewriting, $\displaystyle \frac{z^{2}}{1^{2}}+\frac{y^{2}}{1^{2}}-\frac{x^{2}}{1^{2}}=1\qquad$ this is of the form of a hyperboloid of one sheet, (compare to Table 12.1 and interchange x and z). It opens along the x-axis. In planes parallel to the yz plane ($x=k)$, the cross sections are circles. At $x=0$, the radius is 1 and at $x=\pm 2$, the radius is $\sqrt{5}$ (use for sketching). The cross sections with planes parallel to xy and xz are hyperbolas.