Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. $\begin{array} { l }
x = 3 \cos \theta \
y = 4 \sin \theta
\end{array}$
A) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$
B) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$
C) $y = \frac { x } { 4 }$
D) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$
E) $y = \frac { x } { 3 }$

Question

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.  $\begin{array} { l } 
x = 3 \cos \theta \
y = 4 \sin \theta
\end{array}$ 
A) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$
B) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$
C) $y = \frac { x } { 4 }$
D) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$
E) $y = \frac { x } { 3 }$

Quizplus · Accepted Answer

To eliminate the parameter $\theta$, use the trigonometric identity $\sin^2\theta + \cos^2\theta = 1$. Divide $x = 3\cos\theta$ by 3 and square, and divide $y = 4\sin\theta$ by 4 and square, then add them to get $\frac{x^2}{9} + \frac{y^2}{16} = 1$, which represents an ellipse.

Eliminate the Parameter and Write the Corresponding Rectangular Equation Whose x=3cos⁡θy=4sin⁡θ\begin{array} { l } x = 3 \cos \theta \\y = 4 \sin \theta\end{array}x=3cosθy=4sinθ​

Eliminate the Parameter and Write the Corresponding Rectangular Equation Whose $\begin{array} { l } x = 3 \cos \theta \\y = 4 \sin \theta\end{array}$