1. ## help with these two world problems please

1. A circle C1 of radius 1 rolls counterclockwise along the outside of a circle C2 of radius 4 which is centered at the origin. Assume that there is a point P on the circumference of the circle C1 that sits intially at the point (4,0). Find a parametric curve describing the way that P traces in the plane.

My idea of whats going on: imgur: the simple image sharer

2. For a<0 show that the polar curves $\displaystyle r=asin(t)$ and $\displaystyle r=acos(t)$ intersect at right angles.

2. ## Re: help with these two world problems please

Originally Posted by smoez
1. A circle C1 of radius 1 rolls counterclockwise along the outside of a circle C2 of radius 4 which is centered at the origin. Assume that there is a point P on the circumference of the circle C1 that sits intially at the point (4,0). Find a parametric curve describing the way that P traces in the plane.

My idea of whats going on: imgur: the simple image sharer

2. For a<0 show that the polar curves $\displaystyle r=asin(t)$ and $\displaystyle r=acos(t)$ intersect at right angles.
What have you tried so far?

-Dan

3. ## Re: help with these two world problems please

I figured out #2. As for number one I know it is an Epicycloid and looking at the wiki page I just dont understand how to show in the notation.

4. ## Re: help with these two world problems please

The wiki page does a pretty good job of explaining how they got the equation (see "Proof"). Do you see why the center of the small circle is $\displaystyle (5\cos\theta,5\sin\theta)$? And do you see that $\displaystyle \alpha=4\theta$? From there, it's just a matter of figuring out the coordinates of p.

- Hollywood