Solve the problem.
-Find parametric equations for an object that moves along the ellipse 1 with the motion described. $$\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 81 } = 1$$ The motion begins at $( 3,0 )$, is counterclockwise, and requires 5 seconds for a complete revolution.
A) $x = 3 \cos \left( \frac { 2 \pi } { 5 } t \right) , y = - 9 \sin \left( \frac { 2 \pi } { 5 } t \right) , 0 \leq t \leq 5$
B) $x = - 4 \cos \left( \frac { 2 \pi } { 3 } t \right) , y = 6 \sin \left( \frac { 2 \pi } { 3 } t \right) , 0 \leq t \leq 3$
C) $x = - 3 \cos \left( \frac { 2 \pi } { 5 } t \right) , y = - 9 \sin \left( \frac { 2 \pi } { 5 } t \right) , 0 \leq t \leq 5$
D) $x = 4 \cos \left( \frac { 2 \pi } { 3 } t \right) , y = 6 \sin \left( \frac { 2 \pi } { 3 } t \right) , 0 \leq t \leq 3$

Question

Quizplus · Accepted Answer

The correct parametric equations for an ellipse $\frac{x^2}{9} + \frac{y^2}{81} = 1$ with a counterclockwise motion starting at (3,0) and taking 5 seconds for a complete revolution are $x = 3 \cos \left( \frac{2\pi}{5} t \right)$ and $y = 9 \sin \left( \frac{2\pi}{5} t \right)$, with $0 \leq t \leq 5$. The negative sign in option A for $y$ is incorrect based on the counterclockwise direction, but A is the closest to the correct formulation given the options and the context of the question. The correct formulation should not include a negative sign for $y$, indicating a mistake in the provided options.

Solve the Problem x29+y281=1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 81 } = 19x2​+81y2​=1

Solve the Problem $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 81 } = 1$