How to find simplified rectangular equation?

Question

Eliminate parameter t in the parametric equations below to find a simplified rectangular equation for the curve. 

 

x = 2 sec t

y = tan t

Answer 1

x² = 4 sec²t

    = 4(1 + tan²t)

    = 4 + 4 tan²t

    = 4 + 4y²

 

x² – 4y² = 4

 

If you reduce the above equation to its standard form

x²/2² – y²/1² = 1

 

you will see that it is the equation of a hyperbola centered at (0,0) with a = 2, b = 1 and a horizontal transverse axis.