Question

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

Answer 1

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

Explanation:

x = 1+sint

y = 6+2cost

sint = x-1

cost = (y-6)/2

We know
`sin^(2)t+cos^(2)t=1`

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

`(x-1)^(2)+((y-6)^(2) )/(4)=1`

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.