If students seem stuck on how to explain whether or not the image is an ellipse, you may want to point out that the overlapping circles on the grid help us to count the diagonal distance without having to do any calculations. I am hoping that students will be able to draw on their knowledge of how they made the ellipse out of rope and chalk in the lesson, Human Conics: Circles and Ellipses. Mainly, I want students to be reminded by each other that the sum of distances from each focus point to any point on the ellipse will always have the same value, in this problem 10 cm. I expect students to relate back to how two people in their team had to be foci and one person could be the point on the ellipse and the fact that the rope always retained the same length.
But in case you are interested, there are four curves that can be formed, and all are used in applications of math and science:. Always draw pictures first when working with Conics problems! Before we go into depth with each conic, here are the Conic Section Equations. Note that you may want to go through the rest of this section before coming back to this table, since it may be a little overwhelming at this point!
Conics: Circles, Parabolas, Ellipses, and Hyperbolas
The ancient Greeks recognized that interesting shapes can be formed by intersecting a plane with a double napped cone i. As these shapes are formed as sections of conics, they have earned the official name "conic sections. They are the parabola, the ellipse which includes circles and the hyperbola.
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