Education Technology

Conics In Winter

Activity Overview

Students explore conic graphing using a polar notation equation and determine the effects the various variables on the graph.

Key Steps

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    Students explore how the eccentricity affects the graph of a conic section in polar coordinates. They drag the pointer on a slider to change the value of the eccentricity and observe what happens to the graph.

    They will see that for a parabola the eccentricity is 1, for a hyperbola the absolute value of the eccentricity is greater than 1, and the absolute value of the eccentricity of an ellipse is less than 1.

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    Students go further by exploring the variable d. d represents the distance from the conic section to the directrix. They see how d affects different conic sections. They should also change the value of e and then change the value of d again.

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    Students observe how other changes with the equation will affect the graph. They edit the equation and observe what happens when the plus sign becomes a minus sign and what happens when cosine becomes sine.

    They see that the plus/minus sign reflects the graph about the y-axis. Using cosine results in the graph having a horizontal orientation, and sine results in a vertical orientation.