I have found while teaching students about conic sections that they tend to forget what is going on, and they end up trying to memorize a ton of formulas and equations. I try to give them as many real life examples as I can in hopes that they will understand what conics are instead of just memorizing how to form equations of them. I found a very useful website that I show them as I introduce the section. You can find it
here. Here are just a few examples that the website explains:
Parabolas
canons
satellite dishes
Hyperbolassound waves of a plane intersecting the ground
path of light from a lampshade
I often explain the whispering gallery effect (as in
St. Paul's Cathedral) to help the students grasp the meaning of the focal points of an ellipse.
Math is used in every day life. It may not be in the form you learned from your text, but you do use it.
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