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

question 25

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 \(( 0,5 )\).

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Definitions:

Salpingitis

An inflammation of the fallopian tubes, which can be caused by infection and may lead to infertility if left untreated.

Fallopian Tube

One of a pair of tubes along which eggs travel from the ovaries to the uterus in the female reproductive system.

Pregnancy

The condition of having a developing embryo or fetus in the uterus, marked by various physical and hormonal changes in the body, typically lasting around 40 weeks from the last menstrual period.

Pyuria

The presence of pus in the urine, typically indicating an infection or inflammation in the urinary tract.