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Further Coordinate Systems

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Presentation on theme: "Further Coordinate Systems"— Presentation transcript:

1 Further Coordinate Systems
18 November 2018 Idea ? What would happen if these were two different constants? Def.

2 Equation of an Ellipse 18 November 2018 Idea Ex

3 Equation of an Ellipse 18 November 2018 Ex Page 24 Exercise 2A

4 Tangents and Normals to an Ellipse
18 November 2018 Equations of tangents and normals are most easily found using the parametric form. Idea Ex

5 Tangents and Normals to an Ellipse
18 November 2018 Ex

6 Hyperbolic Functions 18 November 2018 Ex

7 Tangents and Normals to an Ellipse
18 November 2018 Ex Page 27 Exercise 2B

8 Further Coordinate Systems
18 November 2018 ? What would happen if this were subtract rather than add? Def.

9 Further Coordinate Systems
18 November 2018 ? What are the asymptotes of a standard hyperbola?

10 Further Coordinate Systems
18 November 2018 ? What are the two parametric forms for a standard hyperbola?

11 Equation of a Hyperbola
18 November 2018 Ex

12 Equation of a Hyperbola
18 November 2018 Ex Page 30 Exercise 2C

13 Equation of a Hyperbola
18 November 2018 Ex

14 Equation of a Hyperbola
18 November 2018 Ex

15 Equation of a Hyperbola
18 November 2018 Ex

16 Equation of a Hyperbola
18 November 2018 Ex Page 33 Exercise 2D

17 Focus and Directrix 18 November 2018 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 18 November 2018 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 18 November 2018 Idea S

20 Ex Eccentricity Def. The constant e is called the eccentricity
18 November 2018 Def. The constant e is called the eccentricity eccentricity 0 < e < 1 e = 1 e > 1 P describes an ellipse P describes a parabola P describes (half) a hyperbola Ex

21 Eccentricity and the Ellipse
18 November 2018 ? Res. ?

22 Eccentricity and the Ellipse
18 November 2018 Ex

23 Eccentricity and the Ellipse
18 November 2018 Ex

24 Eccentricity and the Hyperbola
18 November 2018 Ex

25 Eccentricity and the Hyperbola
18 November 2018 Ex Page 39 Exercise 2E

26 Rectangular Hyperbola
Coordinate Systems 18 November 2018 ? Complete a table summarising the four coordinate systems you have encountered. Parabola Rectangular Hyperbola Ellipse Standard Hyperbola Cartesian equation Parametric equation General point, P Tangent at P Normal at P

27 Loci associated with conics
18 November 2018 Ex

28 Loci associated with conics
18 November 2018 Ex Page 43 Exercise 2F

29 ? M1 Labels Ex Ex Def. Idea Reference to previous module 1
18 November 2018 M1 Reference to previous module 1 ? Quick Question Def. Definition Idea Key Idea Ex Example Ex Exercise

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