Polar Equations of Conics

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Polar Equations of Conics
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Polar Equations of Conics
Directrix is perpendicular to the polar axis at a distance p units to the left of the pole
Directrix is perpendicular to the polar axis at a distance p units to the right of the pole
Directrix is parallel to the polar axis at a distance p units above the pole
Directrix is parallel to the polar axis at a distance p units below the pole
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Polar Equations of Conics

• Eccentricity
• If e 1, the conic is a parabola the axis of
  symmetry is perpendicular to the directrix
• If e lt 1, the conic is an ellipse the major axis
  is perpendicular to the directrix
• If e gt 1, the conic is a hyperbola the
  transverse axis is perpendicular to the directrix

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Parabola
Directrix x -p Focus Pole
Directrix x p Focus Pole
Directrix y p Focus Pole
Directrix y -p Focus Pole
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Hyperbola


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Hyperbola (cont.)


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Ellipse


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Ellipse (cont.)


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1. Identify the conic that each polar equation
represents. Also, give the position of the
directrix(Similar to p.423 7-12)
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2. Identify the conic that each polar equation
represents. Also, give the position of the
directrix(Similar to p.423 7-12)
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3. Identify the conic that each polar equation
represents. Also, give the position of the
directrix(Similar to p.423 7-12)
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4. Graph the equation(Similar to p.423 13-24)
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5. Graph the equation(Similar to p.423 13-24)
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6. Graph the equation(Similar to p.423 13-24)
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7. Graph the equation
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8. Convert each polar equation to a rectangular
equation(Similar to p.424 25-36)
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9. Convert each polar equation to a rectangular
equation(Similar to p.424 25-36)
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10. Convert each polar equation to a rectangular
equation(Similar to p.424 25-36)