Question

How do you rewrite the two parametric equations’ as one Cartesian equation x = sec(t), y = tan(t), `-pi/2<t<pi/2`?

Answer 1

`y^2 + 1 = x^2`

Explanation:

use the identity `tan^2 + 1 = sec^2`

so here that means that

`y^2 + 1 = x^2`

hyperbola!