Parametric Equations and And a Parameter Interval for the Motion $x=2 \sin t, y=5 \cos t, 0 \leq t \leq 2 \pi$

question 356

Multiple Choice

Parametric equations and and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph
traced by the particle and the direction of motion.
- $x=2 \sin t, y=5 \cos t, 0 \leq t \leq 2 \pi$

• A) \(\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 1\); Counterclockwise from\(( 2,0 )\) to \(( 2,0 )\) one rotation
• B) \(\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 4 } = 1\); Counterclockwise from , \(( 5,0 )\) to \(( 5,0 )\), one rotation
• C) \(\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 4 } = 1\); Counterclockwise from \(( 0,2 )\) to \(( 0,2 )\), one rotation
• D) \(\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 25 } = 1\); Counterclockwise from \(( 0,5 )\) to \(( 0,5 )\), one rotation

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