Describe the Motion of a Particle with Position $( x , y )$

question 51

Multiple Choice

Describe the motion of a particle with position $( x , y )$ as $t$ varies in the given interval $0 \leq t \leq 2 \pi$ .
$$x = 8 \sin t , y = 5 \cos t$$

• A) Moves once counterclockwise along the circle \(x ^ { 2 } + y ^ { 2 } = 1\) starting and ending at \(( 0 , - 5 )\)
• B)
• Moves once counterclockwise along the ellipse \(\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 25 } = 1\) starting and ending at \(( 0,5 )\).
• C)
• Moves once counterclockwise along the ellipse \(\frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 8 } = 1\) starting and ending at \(( - 5,0 )\)
• D)
• Moves once clockwise along the ellipse \(\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 25 } = 1\) starting and ending at \(( 0,5 )\).
• E) Moves once clockwise along the circle \(( 8 x ) ^ { 2 } + ( 5 y ) ^ { 2 } = 1\) starting and ending at \(( 0,5 )\).