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 = 2 + sin(t), y = 4 + 5 cos(t), 𝜋/2 ≤ t ≤ 2𝜋

---------

The motion of the particle takes place on an ellipse centered at
(x, y) =

As t goes from 𝜋/2 to 2𝜋, the particle starts at the point
(x, y) =

and moves clockwise three-fourths of the way around the ellipse to
(x, y) =

Answer 1

the center of
x = a sint
y = b cost
is at (0,0) so your ellipse has center (2,4)

for the other questions, just plug in the values for t. How hard is that?

extra credit: where are the foci?

Answer 2

omg i got it now i just had the worlds massive brainfart