PreCalculus
Activity:
Introduction to Conics
Posted on Feb 18, 2010
Topic: Conics
Students observe how each of the conic sections are formed and connect the locus definition of a parabola with the vertex form of a parabola.
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Activity Key Steps:
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Students will identify how each conic is formed from sectioning cones. Students will use slider arrows to scroll through the different conic sections and visualize how each of the conic sections is formed. They will describe each of these sections.
Next, students will manipulate a point on a parabola and the focus of a parabola to discover the locus definition. Students will use the locus definition to derive the equation of a parabola given the focus, directrix, and any point on the parabola.
Finally, students will manipulate the values in the vertex form of a parabola to observe the effects of each value. Students will describe the relationships among the focus, the directrix, and the values in the vertex form of a parabola.