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Appendix C- Part 2 Graphs of Second Degree Equations

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

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Ellipse

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

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Hyperbola

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Ellipse:

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

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

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

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

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Example:

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Discussion:

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Which axis is the major axis?

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

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Hyperbola:

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Example:

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List equation of the asymptotes:

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Rectangular Hyperbola:

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

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

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

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Recognize shifted conics:

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Recognize shifted rectangular Hyperbola:

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Example: Find equations of both asymptotes:

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Assignment: Page A 23 13-31 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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Section 9.6: Functions and Surfaces Practice HW from Stewart Textbook (not to hand in) p. 683 # 9-13, 19, 20, 23, 24, 25 Handout Sheet 1-6, 7-27 odd.

Section 9.6: Functions and Surfaces Practice HW from Stewart Textbook (not to hand in) p. 683 # 9-13, 19, 20, 23, 24, 25 Handout Sheet 1-6, 7-27 odd.

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