Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.
$\begin{array} { l }
x = 5 \sin 2 \theta \
y = 5 \cos 2 \theta
\end{array}$
A) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 25 } = 1$
B) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 25 } = 1$
C) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 2 } = 1$
D) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 2 } = 0$
E)$y = \frac { x } { 2 }$

Question

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. 
$\begin{array} { l } 
x = 5 \sin 2 \theta \
y = 5 \cos 2 \theta
\end{array}$ 
A) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 25 } = 1$
B) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 25 } = 1$
C) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 2 } = 1$
D) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 2 } = 0$
E)$y = \frac { x } { 2 }$

Quizplus · Accepted Answer

Using the trigonometric identity $\sin^2 \theta + \cos^2 \theta = 1$, we can eliminate the parameter $\theta$ by dividing the equations $x = 5 \sin 2\theta$ and $y = 5 \cos 2\theta$, then squaring both sides and adding them together. This results in $\frac{x^2}{25} + \frac{y^2}{25} = 1$, which matches choice A.

Eliminate the Parameter and Write the Corresponding Rectangular Equation Whose x=5sin⁡2θy=5cos⁡2θ\begin{array} { l } x = 5 \sin 2 \theta \\y = 5 \cos 2 \theta\end{array}x=5sin2θy=5cos2θ​

Eliminate the Parameter and Write the Corresponding Rectangular Equation Whose $\begin{array} { l } x = 5 \sin 2 \theta \\y = 5 \cos 2 \theta\end{array}$