Question: The following statement from a fellow student just a reply to please --
I think that one of the most interesting fields where conic sections are applied is astronomy. As a welder, I had to cut ellipse-shaped holes into the side of tanks routinely.
Although as a matter of personal preference, I tried to incorporate as much math into my job as possible, most of the time it was as easy as just lining up one pipe with the plane that I was intersecting in order to get the proper ellipse shape.
Astronomers on the other hand have not (and still don't) have the luxury of being able to simply hand-measure anything.
The distances that they deal with on a daily basis require them to plot astronomical (pun intended) distances and paths of celestial objects. I think that's pretty amazing.
Please show all your work and give an explanation of steps.