Because first you begin with limits and using them to find derivitives, because derivitives are defined with limits. Not knowing limits will make you clueless to the first half of first year calc.
I have yet to need an oval, and I suspect it will only come up in optics and accoustics Then hyperbole is used a bit (maybe about 1 lecture) in proving the derivitive of lnx (as it is 1/x a hyperbole) and then it is used in hyperbolic trigonometry, which I've only seen in differential equations. Conic sections are important to get mainly at a high level, the most important one I would say is the parabola, because it is everywhere, then the circle, as it has a lot to do with trigonometry, which is in everything and one of the most useful things you will learn. I took pre calc a while ago so I can't remember every topic we went over, but if you ask I can give an opinion.
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