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

Question

Quizplus · Accepted Answer

To find a rectangular equation, we eliminate the parameter $t$. From $x = t^2 + 1$, we get $t^2 = x - 1$. Substituting $t^2$ into $y = t^2 - 1$, we get $y = (x - 1) - 1 = x - 2$. The condition $x \geq 1$ comes from the fact that $t^2 + 1 \geq 1$ for all real $t$.

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