1. Explain how eccentricity determines which conic section is given.
2. If a conic section is written as a polar equation, what must be true of the denominator?
3. If a conic section is written as a polar equation, and the denominator involves , what conclusion can be drawn about the directrix?
4. If the directrix of a conic section is perpendicular to the polar axis, what do we know about the equation of the graph?
5. What do we know about the focus/foci of a conic section if it is written as a polar equation?
For the following exercises, identify the conic with a focus at the origin, and then give the directrix and eccentricity.
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For the following exercises, convert the polar equation of a conic section to a rectangular equation.
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For the following exercises, graph the given conic section. If it is a parabola, label the vertex, focus, and directrix. If it is an ellipse, label the vertices and foci. If it is a hyperbola, label the vertices and foci.
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For the following exercises, find the polar equation of the conic with focus at the origin and the given eccentricity and directrix.
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Equations of conics with an term have rotated graphs. For the following exercises, express each equation in polar form with as a function of .
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Candela Citations
- Precalculus. Authored by: Jay Abramson, et al.. Provided by: OpenStax. Located at: http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1/Preface. License: CC BY: Attribution. License Terms: Download for free at: http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1/Preface