## Calculus (3rd Edition)

Hyperboloid of one sheet; the trace is a hyperbola in the $xz$-plane.
The equation $$\left(\frac{x}{3}\right)^{2}+ \left(\frac{y}{5}\right)^{2} -5z^2=1$$ can rewritten as follows $$\left(\frac{x}{3}\right)^{2}+ \left(\frac{y}{5}\right)^{2} -\left(\frac{z}{\sqrt 5}\right)^{2}=1$$ which is a hyperboloid of one sheet. (See equations on page 691.) To find the trace with the plane $y=1$, we have $$\left(\frac{x}{3}\right)^{2}-\left(\frac{z}{\sqrt 5}\right)^{2}=\frac{24}{25}$$ which is a hyperbola in the $xz$-plane.