Given parametric equations and parameter intervals for the motion of a particle

Question

Given parametric equations and parameter intervals for the motion of a particle in the xy - plane below, 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 cos (t), y = sin (t): 0 lessthanorequalto t lessthanorequalto 2 pi Choose the correct Cartesian equation which represents the same path defined by the parametric equations. A. x^2 + y^2/4 = 1 B. x^2/4 + y^2 = 1 C. x^2 + y^2 = 4 D. x^2 + y^2 = 2

Explanation / Answer

We have x = 2cos (t) or, x/2 = cos (t) and y = sin(t) 0 t 2. Then (x/2)2 +y2 = cos2(t) +sin2(t) or, (x2/4)+y2 = 1 ( as cos2(t) +sin2(t) = 1). Thus, the answer is (x2/4)+y2 = 1.Option B is the correct answer.

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