Sketch the parametric curve for x=6cost and y=2sint for 0≤t≤2π. Indicate the direction of motion.

Question

Sketch the parametric curve for x=6cost and y=2sint for 0≤t≤2π. Indicate the direction of motion.

Answer 1

x/3 = 2cost and y = 2sint

So, (x/3)² + y² = 4cos²t + 4sin²t = 4(cos²t + sin²t) = 4

x² / 36 + y² / 4 = 1

This is an ellipse centered at (0, 0) with horizontal major axis of length 12 and

vertical minor axis of length 4.

The direction of motion is counterclockwise.

Answer 2

x=6cost

y=2sint

x^2 +9y^2= 36cos^2(t) + 36sin^2(t)=36

x^2 + 9y^2 = 36

x^2/36 + y^2/4 = 1, an ellipse, center at the origin,

major axis from (6,0) to (-6,0), minor axis from (0,2) to (0,-2)