We are doing conic sections, and the practice problems are pretty easy, far too east to be on on of our tests. Can someone give me an example of what I might be asked to find and from what information in a difficult conics question?
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Are you approaching it from a geometric standpoint, an algebraic standpoint, or some combination of the two? And is this for a high school class, a college class? Have you had or are you taking calculus?
No, this is a pre-calculus high school course, and we approach them both from a geometric and algebraic standpoint. We examined what angles a plane must cut a conic in order to form certain shapes, and we study the graphs of those shapes algebraically.
I took this last year. I'll check my notebook real quick.
The first thing you should do is geometry of the ellipse, the focal constant and the sum of the two focal radii is constant.
Unfortunately I haven't learned Latex yet but i'll give the terminology.
You'll learn the equation of an ellipse graph and the equation of a hyperbola, both are almost identical. Then of course you'll need to graph them yourself but it's not that difficult. We didn't have to plug in or anything, we learned a few tricks that allow you to graph them quickly and accurately.
We were then asked to compute the focal constant (the equation looks a lot like pythagoras' theorem).
The hardest part I found was computing and graphing conic sections via the general conic section equation (rearranging into the standard equation that can be used to graph easily) which generally requires the use of completing the square, so brush up on that if necessary.
((x-h)^2)/a^2 + ((y-k)^2)/b^2 = 1 is the formula template that we had to end up with to graph conic sections easily (for hyperbolas you just change the plus in the middle to a minus). Sorry I can't put it into latex, I should probably go learn it.
After that it was all practice for me, I can't gartuntee it's the same as you'll do. These are the basics, we learned a lot of tricks and shortcuts. We didn't spend much time on the terminology, but I can't gartuntee that you won't either.