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Appendix C- Part 2 Graphs of Second Degree Equations.

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Presentation on theme: "Appendix C- Part 2 Graphs of Second Degree Equations."— Presentation transcript:

1 Appendix C- Part 2 Graphs of Second Degree Equations

2 Today, we will review 2nd Degree equations such as:

3

4 Ellipse

5 Today, we will review 2nd Degree equations such as:

6 Hyperbola

7 Ellipse:

8

9 If the equation can be placed in this form, then:

10 Ellipse: If the equation can be placed in this form, then:

11 Ellipse: If the equation can be placed in this form, then:

12 Ellipse: If the equation can be placed in this form, then:

13 Example:

14

15

16 Discussion:

17 Which axis is the major axis?

18 Discussion: Which axis is the major axis? Length of the major axis is always?

19 Hyperbola:

20

21

22

23 Example:

24 List equation of the asymptotes:

25 Rectangular Hyperbola:

26

27 If k is a positive value, then the curve lies in quadrants 1 and 3.

28 Rectangular Hyperbola: If k is a negative value, then the curve lies in quadrants 2 and 4.

29 Rectangular Hyperbola: All curves of this type have asymptotes with equations: x = 0 and y = 0

30 Recognize shifted conics:

31

32 Recognize shifted rectangular Hyperbola:

33

34 Example: Find equations of both asymptotes:

35 Assignment: Page A odd, 35 Make sketches for 13 – 21 odd and for the rest just identify the type of curve (hyperbola, ellipse, circle, or parabola).


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