Answer
(a) ellipsoid.
(b) hyperboloid of one sheet.
(b) hyperboloid of two sheets.
Work Step by Step
(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.)
