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Describe the motion of a particle with position (x, y) as t varies in the given interval. (For each answer, enter an ordered pair of the form x, y.) x = 1 + sin(t), y = 6 + 2 cos(t), π/2 ≤ t ≤ 2π

Respuesta :

Answer:

Path followed by the particle is an incomplete ellipse whose points do not lie on first quadrant.

Step-by-step explanation:

x = 1+sint

y = 6+2cost

sint = x-1

cost = (y-6)/2

We know [tex]sin^{2}t+cos^{2}t=1[/tex]

Substituting for sint and cost in the above equation,we get:

[tex](x-1)^{2}+\frac{(y-6)^{2} }{4}=1[/tex]

The above equation represents an ellipse with center at (1,6) with major axis length as 4 and minor axis length as 2.

But since π/2 ≤ t ≤ 2π

It represents an incomplete ellipse which does not have any points on the first quadrant.