Find a rectangular equation for the plane curve defined by the parametric equations.
-$$x = 3 \tan t , y = 2 \sec t ; 0 \leq t \leq 2 \pi$$
A) $y = x ^ { 2 } - 9$; for $x$ in $- 3 \leq x \leq 3$
B) $y = 3 \sqrt { 1 + \frac { x ^ { 2 } } { 25 } }$; for $x$ in $- \infty

Question

Find a rectangular equation for the plane curve defined by the parametric equations.
-$$x = 3 \tan t , y = 2 \sec t ; 0 \leq t \leq 2 \pi$$
A) $y = x ^ { 2 } - 9$; for $x$ in $- 3 \leq x \leq 3$
B) $y = 3 \sqrt { 1 + \frac { x ^ { 2 } } { 25 } }$; for $x$ in $- \infty < x < \infty$
C) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$; for $x$ in $- \infty < x < \infty$
D) $\frac { y ^ { 2 } } { 9 } + \frac { x ^ { 2 } } { 25 } = 1$; for $x$ in $- \infty < x < \infty$

Quizplus · Accepted Answer

The correct answer is C because it is the only equation that is satisfied by the parametric equations for all values of t in the given interval.

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