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.

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Presentation transcript:

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

Polar Equations of Conics Eccentricity If e = 1, the conic is a parabola; the axis of symmetry is perpendicular to the directrix If e < 1, the conic is an ellipse; the major axis is perpendicular to the directrix If e > 1, the conic is a hyperbola; the transverse axis is perpendicular to the directrix

Parabola Directrix: x = -p Focus: Pole Directrix: x = p Focus: Pole Directrix: y = p Focus: Pole Directrix: y = -p Focus: Pole

Hyperbola

Hyperbola (cont.)

Ellipse

Ellipse (cont.)

1. Identify the conic that each polar equation represents. Also, give the position of the directrix (Similar to p.423 #7-12)

2. Identify the conic that each polar equation represents. Also, give the position of the directrix (Similar to p.423 #7-12)

3. Identify the conic that each polar equation represents. Also, give the position of the directrix (Similar to p.423 #7-12)

4. Graph the equation (Similar to p.423 #13-24)

5. Graph the equation (Similar to p.423 #13-24)

6. Graph the equation (Similar to p.423 #13-24)

7. Graph the equation

8. Convert each polar equation to a rectangular equation (Similar to p.424 #25-36)

9. Convert each polar equation to a rectangular equation (Similar to p.424 #25-36)

10. Convert each polar equation to a rectangular equation (Similar to p.424 #25-36)