See below and explain fully. Describe the motion of a particle with position P(x

Question

See below and explain fully.

Describe the motion of a particle with position P(x, y) when x = 4 sin t, y = 5 cost as t varies in the interval 0 le t le 2pi. Moves once counterclockwise along the ellipse (4x)2 + (5y)2 = 1, starting and ending at (0, 5). Moves once clockwise along the ellipse x2 / 16 + y2 / 25 = 1, starting and ending at (0,5) Moves along the line x / 4 + y / 5 = 1, starting at (4, 0) and ending at (0, 5). Moves once clockwise along the ellipse x 2 / 16 + y 2 / 25 = 1, starting and ending (0. 5). Moves along the line x / 4 + y / 5 = 1, starting at (0,5) and ending at (4,0). Moves once clockwise along the ellipse (4x)2 + (5y)2 = 1, starting and ending at (0, 5).

Explanation / Answer

x = 4sint;y=5cost

x/4 = sint; y/5 = cost;

as sin^2t + cos^2t = 1

=> (x/4)^2+(y/5)^2 = 1

or x^2/16 + y^2/25 =1 which is equation of an ellipse

at t=0; x=0 and y=5; on y axis

for t=0+, x and y both are positive,i.e in first quadrant

=> particle is moving clockwise

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