Eliminating the parameter and write the resulting rectangular equation

Question

Consider the following. x=2 sec(𝜃) y=tan(𝜃) 𝜋/2 < 𝜃 < 3𝜋/2

Eliminate the parameter and write the resulting rectangular equation whose graph represents the curve.

Answer 1

x = 2 sec θ => cos θ = 2/x and then sin θ = [sqrt(x² - 4)]/x

y = (sin θ)/cos θ and substitution gets y=.5sqrt(x² - 4)