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) $y = \frac { x } { 2 }$

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) $y = \frac { x } { 2 }$

Quizplus · Accepted Answer

The parameterization of the curve is given by 
$$
x=3\sin t,\ y=3\cos t
$$
We can use the Pythagorean identity $\sin^2t+\cos^2t=1$ to eliminate $t$:
$$
x^2+y^2 = (3\sin t)^2 + (3\cos t)^2 = 9(\sin^2t+\cos^2t) = 9
$$
This is the equation of a circle with center at the origin and radius $3$.

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 $\begin{array} { l } x = 5 \sin 2 \Theta \\y = 5 \cos 2 \theta\end{array}$