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Further Coordinate Systems

?. What would happen if these were two different constants?. Def. Further Coordinate Systems. Idea. Ex. Equation of an Ellipse. Idea. Equation of an Ellipse. Ex. Page 24 Exercise 2A. Ex. Tangents and Normals to an Ellipse.

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Further Coordinate Systems

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  1. ? What would happen if these were two different constants? Def. Further Coordinate Systems Idea

  2. Ex Equation of an Ellipse Idea

  3. Equation of an Ellipse Ex Page 24 Exercise 2A

  4. Ex Tangents and Normals to an Ellipse Equations of tangents and normals are most easily found using the parametric form. Idea

  5. Tangents and Normals to an Ellipse Ex

  6. Hyperbolic Functions Ex

  7. Tangents and Normals to an Ellipse Ex Page 27 Exercise 2B

  8. ? What would happen if this were subtract rather than add? Def. Further Coordinate Systems

  9. Further Coordinate Systems ? What are the asymptotes of a standard hyperbola?

  10. Further Coordinate Systems ? What are the two parametric forms for a standard hyperbola?

  11. Equation of a Hyperbola Ex

  12. Equation of a Hyperbola Ex Page 30 Exercise 2C

  13. Equation of a Hyperbola Ex

  14. Equation of a Hyperbola Ex

  15. Equation of a Hyperbola Ex

  16. Equation of a Hyperbola Ex Page 33 Exercise 2D

  17. Focus and Directrix A parabola is the locus of points equidistant between a fixed point (the focus) and a fixed line (the directrix) FP1

  18. Focus and Directrix A parabola is the locus of points P(x, y) equidistant between a fixed point S (the focus) and a fixed line (the directrix) FP1 S

  19. Focus and Directrix Idea S

  20. eccentricity 0 < e < 1 P describes an ellipse e = 1 P describes a parabola e > 1 P describes (half) a hyperbola Eccentricity Def. The constant e is called the eccentricity Ex

  21. Res. ? Eccentricity and the Ellipse ?

  22. Eccentricity and the Ellipse Ex

  23. Eccentricity and the Ellipse Ex

  24. Eccentricity and the Hyperbola Ex

  25. Eccentricity and the Hyperbola Ex Page 39 Exercise 2E

  26. Coordinate Systems ? Complete a table summarising the four coordinate systems you have encountered.

  27. Loci associated with conics Ex

  28. Loci associated with conics Ex Page 43 Exercise 2F

  29. Labels M1 Reference to previous module 1 ? Quick Question Def. Definition Idea Key Idea Ex Example Ex Exercise

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