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Conic Section In Geogebra

Instructions: A conics section is a curve obtained as the intersection of the surface of a cone with a plane. To make a conic section we take slices of a "double-napped" cone. Here we have a "double-napped" cone with the intersecting plane, p. We can move the points making up plane p in order to further explore conic sections. While exploring think about the following: What is a conic section? How do we construct a conic section in Geogebra? What is the standard form of the equation for each conic section? Where do these equations come from?
Prompts: 1. Find the following conic section: the hyperbola, the parabola, and the ellipse; the circle. 2..Explore the positions of the points that make up plane p and make a conjecture about how the points positions affect the type of conic. 3. Explore the conic sections ellipse and circle. A circle is a special type of ellipse, how did what you explore deepen your understanding of this statement.