Let x = a sec t and y = b tan t.
(a) Let a = 1, 2, or 3, b = 1,2, or 3, and graph using the parameter interval (-π/2, π/2). Explain what you see, and describe the role of a and b in these parametric equations. (Caution: If you get what appear to be asymptotes, try using the approximation [-1.57, 1.57] for the parameter interval.)

(b) Let a = 2,b = 3, and graph in the parameter interval
(π/2, 3π/2). Explain what you see.

(c) Let a = 2, b = 3, and graph using the parameter interval (-π/2, 3π/2). Explain why you must be careful about graphing in this interval or any interval that contains ± π/2.

(d) Use algebra to explain why

(e) Let x = a tan t and y = b sec t. Repeat (a), (b), and (d) using an appropriate version of (d).

(() a b 1.