Find a rectangular equation for the plane curve defined by the parametric equations.
-$x = \sec t , y = \tan t$
A) $x ^ { 2 } - y ^ { 2 } = 1$
B) $y = x + 1$
C) $y ^ { 2 } - x ^ { 2 } = 1$
D) $\mathrm { y } = \mathrm { x } - 1$

Question

Quizplus · Accepted Answer

Using trigonometric identities, we know that $\sec^2 t - \tan^2 t = 1$. Substituting $x = \sec t$ and $y = \tan t$ into this identity gives us $x^2 - y^2 = 1$, which matches option A.

Find a Rectangular Equation for the Plane Curve Defined by the Parametric