I can give you some help with the applications part of the question.
In the Resource Room section of Math Central there is an article titled Why are satellite dishes parabolic? The reflective property of the parabola that is described in this article is also used in some telescopes. This same property leads to applications of the parabola for transmission as well as collecting. The reflector behind the light bulb in some automobile headlights and data projectors is parabolic in shape so that the reflected light doesn't scatter in different directions.
Go to the first page of Math Central and follow the link to math beyond school. In the search window type in conic and you will find some applications of ellipses, hyperbolas and circles. In fact all of trigonometry is based on circles so any application of trigonometry is actually an application of circles also.
I hope this helps,