Hyperbolas [Recovered]

Algebra II hyperbolas
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Hyperbolas [Recovered]

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  1. Hyperbola

    Slide 1 - Hyperbola

    • A and C are opposite signs
    • Both squared terms have opposite signs
  2. Horizontal Hyperbola:

    Slide 2 - Horizontal Hyperbola:

    • Center (h,k)
    • a
    • Vertex
    • a
    • Vertex
    • b
    • b
    • c
    • Focus
    • c
    • Focus
    • Plus!
    • Transverse Axis
  3. Vertical Hyperbola:

    Slide 3 - Vertical Hyperbola:

    • Plus!
    • Notice!
    • Center (h,k)
    • a
    • Vertex
    • a
    • Vertex
    • b
    • b
    • c
    • Focus
    • c
    • Focus
    • Transverse Axis
  4. Center:

    Slide 4 - Center:

    • Vertices:
    • Length of Transverse Axis:
    • Asymptotes:
    • Eccentricity:
    • Horizontal Hyperbola
    • (always > 1 for hyperbola)
  5. Ex. 2

    Slide 5 - Ex. 2

    • Complete the Square to change to Vertex Form
    • Group x2 and x, group y2 and y, move constant to other side
    • Factor coefficients of x2 and y2
    • Complete the square twice
  6. Slide 6

    • Add the product of the coefficient of x2 and 1, as well as the product of the coefficient of y2 and 36 to the right side ONLY!!
    • Factor Perfect Square Trinomials
    • Divide both sides by the constant term
  7. Center:

    Slide 7 - Center:

    • Vertices:
    • Length of Transverse Axis:
    • Asymptotes:
    • Eccentricity:
    • Vertical Hyperbola
    • (always > 1 for hyperbola)
  8. Ex. 3 Find the equation of a hyperbola with asymptotes

    Slide 8 - Ex. 3 Find the equation of a hyperbola with asymptotes

  9. Try on Your Own!!

    Slide 9 - Try on Your Own!!

    • 1.  Determine if each hyperbola is vertical or horizontal:
    • 2.  Write this hyperbola’s equation in vertex form: 
    • 3.  Graph the following hyperbola.  State the center, foci, length of transverse axis, vertices, equations of asymptotes, and eccentricity.