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

question 100

Multiple Choice

Solve the problem.
-Find parametric equations for an object that moves along the ellipse $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 81 } = 1$ with the motion described.
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) \(x = 4 \cos \left( \frac { 2 \pi } { 3 } t \right) , y = 6 \sin \left( \frac { 2 \pi } { 3 } t \right) , 0 \leq t \leq 3\)

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