# Equation of the path of the particle

1. Jun 22, 2013

### skybox

1. The problem statement, all variables and given/known data
The x and y coordinates of a particle moving in the x-y plane are $$x=8sin(t)$$ and $$y=6cos(t)$$. What is the equation of the path of the particle?

2. Relevant equations
$$m=\frac{y_2-y_1}{x_2-x_1}$$
$$y-y_1=m(x-x_1)$$

3. The attempt at a solution
I am stuck on how to approach this problem.
I drew a picture:
. Can I use one point as the origin, (0,0) and the second point as (8sint, 6cost) and use the equation of a line to find the 'path' of the particule? I am confused if the path of the particule means the equation of the line?

Any tips and hints would be great. Thanks!

2. Jun 22, 2013

### tiny-tim

hi skybox!
no, the path of the particle means the curve joining all the points (8sint, 6cost)

(if you're still stuck, come back for a hint)

3. Jun 22, 2013

### skybox

Thanks tiny-tim. After some research, looks like this is a parametric equation. Since it has cosines and sines, it will most likely be a circle or ellipse from $$0<=x<=2\pi$$.

I will try to solve this and post the solution when done. Thanks again!

4. Jun 22, 2013

### skybox

I was able to solve it! Attached is the solution (as an image I did in Word) if anyone is interested.

#### Attached Files:

• ###### solution.PNG
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7.4 KB
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490
5. Jun 23, 2013

### tiny-tim

me! me! i'm interested!

yes, nicely done

(btw, for a lot of purposes, the form x2/a2 + y2/b2 = 1 is preferred, so you could have stopped there)