## Calculus (3rd Edition)

(a) When all signs are "+", we get $$\left(\frac{x}{1/\sqrt 8}\right)^{2}+\left(\frac{y}{1/\sqrt 3}\right)^{2}+z^{2}=1$$ which is an ellipsoid. (b) When two signs are "+", we get $$\left(\frac{x}{1/\sqrt 8}\right)^{2}+\left(\frac{y}{1/\sqrt 3}\right)^{2}-z^{2}=1$$ which is a hyperboloid of one sheet. (b) When one sign is "+", we get $$\left(\frac{x}{1/\sqrt 8}\right)^{2}-\left(\frac{y}{1/\sqrt 3}\right)^{2}-z^{2}=1$$ which is a hyperboloid of two sheets. (See equations on page 691-692.)