i haven't had trigonometry in years. enjoy.
to clarify, imagine two cones stacked on their points. now imagine you sliced through them at some angle. you'll either get closed shapes or open curves. hyperbolas and parabolas are cutting the cone closer to a vertical angle. ellipses and circles are when you cut closed to a horizontal angle. there's a ton of info you should have payed attention to in class with the focuses and directrix and such. enjoy homework.