# Thread: Motion in the xy-plane -- ahhhh

1. ## Motion in the xy-plane -- ahhhh

Hey, I just found this forum and I could use some help

The directions read: r(t) is the position of a particle in the xy-plane at time t. Fomd am equation in x and y whose graph is the path of the particle.

the original problem: r(t) = (cos2t)i + (3sin2t)j

so far, I have:

x = cos2t
y = 3sin2t

Now I know i have to set they equal to each other, but I can't seem to figure out how to solve one of them for t. Any help would be much appreciated!

Thanks!

2. Originally Posted by oxx
Hey, I just found this forum and I could use some help

The directions read: r(t) is the position of a particle in the xy-plane at time t. Fomd am equation in x and y whose graph is the path of the particle.

the original problem: r(t) = (cos2t)i + (3sin2t)j

so far, I have:

x = cos2t
y = 3sin2t

Now I know i have to set they equal to each other, but I can't seem to figure out how to solve one of them for t. Any help would be much appreciated!

Thanks!
$x = cos2t$
$y = 3sin2t\implies\frac{y}{3}=sin2t$

Eliminate t from these 2 equations using $cos^22t+sin^22t=1$.

3. Thanks, I think that helped a lot.

I got an answer of y = 3 (1 +x^2)^(1/2)

does that look right?

4. Actually it is x^2 + (y^2)/9 = 1

which is an ellipse

The formula you gave is only the upper half.

The parametric eqns generate the entire ellipse as t varies from 0 to pi