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Conic Sections in Polar Coordinates

Conic Sections in Polar Coordinates. Lesson 10.6. If the ratio of the two distances is different from 1, other curves result. Definition of Parabola. Set of points equal distance from a point and a line Point is the focus Line is the directrix. •. d( P, F ). •. d( P, L ).

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Conic Sections in Polar Coordinates

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  1. Conic Sections in Polar Coordinates Lesson 10.6

  2. If the ratio of the two distances is different from 1, other curves result Definition of Parabola • Set of points equal distancefrom a point and a line • Point is the focus • Line is the directrix •

  3. d(P, F) • d(P, L) General Definition of a Conic Section • Given a fixed line L and a fixed point F • A conic section is the set of all points P in the plane such that • F L Note: This estands for eccentricity. It is not the same as e = 2.71828

  4. General Definition of a Conic Section • When e has differentvalues, different curvesresult • 0 < e < 1 The conic is an ellipse • e = 1 The conic is a parabola • e > 1 The conic is a hyperbola • Note: The distances are positive • e is always greater than zero

  5. Polar equations of Conic Sections • A polar equation that has one of the following forms is a conic section • When cos is used, major axis horizontal • Directrix at y = p • When sin is used, major axis vertical • Directrix at x = p

  6. Example • Given • Identify the conic • What is the eccentricity? • e = ______ • Graph the conic Note the false asymptotes

  7. Special Situation • Consider • Eccentricity = ? • Conic = ? • Now graph • Note it is rotated by-π/6

  8. 5 • 1 y = - 5 Finding the Polar Equation • Given directrix y = -5 and e = 1 • What is the conic? • Which equation to use?

  9. Assignment • Lesson 10.6 • Page 438 • Exercises 1 – 19 odd

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