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Hyperbolas

Unit 1 Test-Tues. Hyperbolas. Objective: SWBAT find the standard form of a hyperbola and identify its key features . SWBAT graph a hyperbola and identify its key features. SWBAT identify the conic and state its unique features.

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Hyperbolas

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  1. Unit 1 Test-Tues Hyperbolas Objective: SWBAT find the standard form of a hyperbola and identify its key features. SWBAT graph a hyperbola and identify its key features. SWBAT identify the conic and state its unique features. Hwk #6: pg 663 #1-9 odd, 23-39 EOO, 41Answer Key in book wrong for

  2. Definition - Hyperbola: • the set of all points P(x, y) in a plane such that the absolute value of the difference between the distance from P to two fixed points in the plane F1 and F2, called the foci, is constant.

  3. A hyperbola has 2 axes of symmetry: • Transverse axis – length = 2a • Conjugate Axis – length = 2b • Vertices - endpoints of the transverse axis • Co-vertices - endpoints of the conjugate axis • Foci are always on the transverse axis • Center - the point of intersection of the 2 axes

  4. Horizontal Transverse Axis • Standard form: • Center: • Vertices: • Co-vertices: • Foci: • Asymptotes:

  5. Example of asymptotes

  6. Eccentricity • The eccentricity of a hyperbola is the ratio of c to a and always greater than 1.

  7. 1) Find the center, vertices, foci and asymptotes.

  8. Vertical Transverse Axis • Standard form: • Center: • Vertices: • Co-vertices: • Foci: • Asymptotes:

  9. Relationship with a and b? • In a hyperbola the transverse axis is not necessarily the longest (like it was for ellipses). The key to determine which is the transverse axis is to look at the equation of which comes first (or is positive).

  10. 2) Write in standard form.

  11. 3) Write in standard form • Vertices: (-2, 3) (4, 3) • Co-vertices: (1,1) (1, 5)

  12. 4) Write in standard form • Co-vertices: (-3, 1) (7, 1) • Foci: (2, 1- ) (2, 1+ )

  13. 5) Write in standard form

  14. 6) Write in standard form

  15. Graphing a Hyperbola

  16. Test info!! • We will take the test after lunch, so ask any questions prior to lunch. • Extra practice worksheets answers are online. • Test includes an extra credit and a smart point opportunity. • No equations of asymptotes on the test 

  17. Exit Slip • Write the standard equation for the hyperbola with the given characteristics. • Center (-1, 4) • Vertex (-1, 6) • Co-vertex (-3, 4)

  18. Review sheet • Work to complete the review sheet.

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