Conics - Hyperbola

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  1. Hyperbola:
    horizontal hyperbola horizontal hyperbola
    vertical hyperbola vertical hyperbola

    • Graph looks sort of like two mirrored parabolas, with the two "halves" being called "branches".
    • "Vertices" are defined similarly to the way of a "vertex" is defined for a parabola.
    • Just as the focus for a parabola, the two foci for a hyperbola are inside each branch.
    • The line connecting the two vertices is called the "transverse axis".
  1. properties of a hyperbola
    (x64)2+(y+53)2=1 -(\frac{x-6}{4})^2 + (\frac{y+5}{3})^2=1
    1. Identify the type of conic section.
    2. State the "center".
    3. Set up the guidelines for the conic graph.
    4. Find the "vertices".
    5. Locate the "foci".
    6. Find the "eccentricity".
    7. Find the equations of the "asymptotes".
    8. Find the lengths of transverse axis and conjugate axis.
Topic Notes
hyperbola: the difference of the distances from any point on a hyperbola to each focus is constant and equal to the transverse axis 2a2a.
ellipse: the sum of the distances from any point on an ellipse to each focus is constant and equal to the major axis 2a2a.

c=a2b2c= \sqrt{a^2 - b^2} cc: distance from the center to a focus

e=cae= \frac{c}{a} ee: eccentricity; the larger the value of ee, the straighter the hyperbola