Definition

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Definition
A hyperbola is the set of all points such that
the difference of the distance from two given
points called foci is constant
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Definition
The parts of a hyperbola are
transverse axis
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Definition
The parts of a hyperbola are
conjugate axis
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Definition
The parts of a hyperbola are
center
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Definition
The parts of a hyperbola are
vertices
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Definition
The parts of a hyperbola are
foci
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Definition
The parts of a hyperbola are
the asymptotes
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Definition
The distance from the center to each vertex is a
units
a
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Definition
The distance from the center to the rectangle
along the conjugate axis is b units
b
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Definition
The distance from the center to each focus is c
units where
c
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Sketch the graph of the hyperbolaWhat are the
coordinates of the foci?What are the coordinates
of the vertices?What are the equations of the
asymptotes?
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How do get the hyperbola into an up-down
position?
switch x and y
identify vertices, foci, asymptotes for
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Definition
Standard equations
where (h,k) is the center
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Definition
The equations of the asymptotes are
for a hyperbola that opens left right
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Definition
The equations of the asymptotes are
for a hyperbola that opens up down
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Summary

• Vertices and foci are always on the transverse
  axis

• Distance from the center to each vertex is a units

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Summary

• If x term is positive, hyperbola opens left
  right

• If y term is positive, hyperbola opens up down

• a2 is always the positive denominator

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Example
Find the coordinates of the center, foci, and
vertices, and the equations of the asymptotes for
the graph of
then graph the hyperbola.
Hint re-write in standard form
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Solution
Center (-3,2) Foci (-3 ,2)
Vertices (-2,2), (-4,2)
Asymptotes
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Example
Find the coordinates of the center, foci, and
vertices, and the equations of the asymptotes for
the graph of
then graph the hyperbola.
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Solution
Center (-4,2) Foci (-4,2 )
Vertices (-4,-1), (-4,5)
Asymptotes