Conic Sections are all around us, and they make up a ton of what we see and use daily.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
Let’s take a closer look at some of the foods that we eat.
If you slice an orange, it’s cross section is a circle! How about an egg or a watermelon? Yep, you guessed it…an ellipse!
How about some of the games we play?
A Basketball, baseball, tennis ball, etc., all have a circular cross section. And a football has cross-sectional slices like an ellipse!
Do you like boardgames?
Well, I do! Have you ever played a game with an hourglass timer? Well, our friend the hyperbola traces the hourglass perfectly!
Ever been horseback riding or seen a horse’s saddle. Well, the saddle is also comprised of hyperbolas! Astonishing!
Now, what about your everyday household items? Take a cereal bowl or a large coffee mug or even some flower vases. They have cross-sectional slices like a parabola!
Gosh, look at all the math, in particular all those conic sections, that surrounds you on a daily basis!
Conic Section Properties
So now that we know that Conic Sections play a significant role in our daily lives let’s make sure we can recognize them from various equations, because this knowledge is going to be so super-duper helpful for when see 3D conic sections again in Multivariable Calculus!
We’re going to start off by looking at their most important features and be able to identify each conic section (Parabola, Circle, Ellipse, or Hyperbola) without graphing. Again, we aren’t going to focus too much on their specifics, because our goal is to recognize the Conic just by its equation.
For a similar list of features can be found at Math2.
Then we are going to investigate a particular group of Conics called Half-Conics, sometimes referred to as Half-Graphs or Semiconics.
They graphs are just “half” of the original, so only half a circle or half an ellipse, etc. We’ll learn how to spot them, graph them and also provide their domain and range.
Wow, what a fun lesson!
Conics Review – Video
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