A New Look at Conic Sections

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Presentation transcript:

A New Look at Conic Sections If P is a point in the plane, of d and F, the set of points for which the ratio PF:PD is the constant e. The number e is the eccentricity of a conic section. A set of points is: An ellipse if 0 < e <1 A parabola if e = 1 A hyperbola if e > 1 In an ellipse as the eccentricity of the ellipse approaches 0, the ellipse becomes more circular. The eccentricity of a circle is 0.

Example 1. Let the focus F be (0, 3) and let the directrix d have equation y = 12. Find the equation of the set of points P for which , and identify the graph.

Example 2. Identify the graph of the equation