When do the curves $r=a(1+\sin\theta)$ $r=a(1-\sin\theta)$ intersect? By converting the equations to $x$- and $y$-components, and setting them equal, I get they intersect at $\theta=0,\pi$, giving the points $(a,0)$ and $(a,\pi)$. But I don't get the point $(0,0)$--how would I find that?

the third point of intersection happens when $\theta = 3\pi/2, r_1 = 0$  and $\theta = \pi/2, r_2 = 0.$ that is the point $r = 0$ in polar coordinates and $(0,0)$ in cartesian coordinates.
