# Show that he object moves on an elliptical path

1. Nov 21, 2009

### Saladsamurai

Okay then

1. The problem statement, all variables and given/known data

An object moves in the xy-plane such that its position vector is

$$\bold{r} = \bold{i}a\cos(\omega t)+\bold{j}b\sin(\omega t) \qquad (1)$$

where a,b, and $\omega$ are constants.

Show that the object moves on the elliptical path

$$(\frac{x}{a})^2+(\frac{y}{b})^2 =1 \qquad (2)$$

I have never studied ellipses, so I am 'googling' them now as we speak. I can see that (2) resembles the equation of a circle except that it includes a couple of scaling factors 'a' and 'b'.

I am just not sure how to relate (1) and (2) to each other.

Can I get a friendly 'nudge' here?

Thanks!

~Casey

2. Nov 21, 2009

### Feldoh

$$\bold{r} = \bold{i}a\cos(\omega t)+\bold{j}b\sin(\omega t) = \bold{i}x +\bold{j}y$$

Right?

So $$x = a\cos(\omega t), y = b\sin(\omega t)$$

Just plug it in to the equation (2) in order for it to hold it must hold for all t.

3. Nov 21, 2009

### Saladsamurai

Right. I thought I was making it more difficult than it is. I don't know why I thought that there was something more to it. Thanks again!

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