Question

A pair of parametric equations is given.

x=sec(t), y=tan^2(t), 0 <= t <= pi/2

Find a rectangular-coordinate equation for the curve by eliminating the parameter.

Answer 1

x2=1+y

Answer 2

\[ y = \tan^2t = \sec^2t - 1 = x^2 - 1\]
\[ y+1 = x^2 \]

Answer 3

x belonging to [0,inf)