A hyperbola is the collection of points in the plane the difference of whose distances from two fixe

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A hyperbola is the collection of points in the
plane the difference of whose distances from two
fixed points, called the foci, is a constant.
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Theorem Equation of a Hyberbola Center at (0,
0) Foci at ( c, 0) Vertices at ( a, 0)
Transverse Axis along the x-Axis
An equation of the hyperbola with center at (0,
0), foci at ( - c, 0) and (c, 0), and vertices at
( - a, 0) and (a, 0) is
The transverse axis is the x-axis.
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Theorem Equation of a Hyberbola Center at (0,
0) Foci at ( 0, c) Vertices at (0, a)
Transverse Axis along the y-Axis
An equation of the hyperbola with center at (0,
0), foci at (0, - c) and (0, c), and vertices at
(0, - a) and (0, a) is
The transverse axis is the y-axis.
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Theorem Asymptotes of a Hyperbola
The hyperbola
has the two oblique asymptotes
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Theorem Asymptotes of a Hyperbola
The hyperbola
has the two oblique asymptotes
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Find an equation of a hyperbola with center at
the origin, one focus at (0, 5) and one vertex at
(0, -3). Determine the oblique asymptotes.
Graph the equation by hand and using a graphing
utility.
Center (0, 0)
Focus (0, 5) (0, c)
Vertex (0, -3) (0, -a)
Transverse axis is the y-axis, thus equation is
of the form
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25 - 9 16
Asymptotes
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V (0, 3)
F(0, 5)
(4, 0)
(-4, 0)
F(0, -5)
V (0, -3)
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Hyperbola with Transverse Axis Parallel to the
x-Axis Center at (h, k) where b2 c2 - a2.
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Hyperbola with Transverse Axis Parallel to the
y-Axis Center at (h, k) where b2 c2 - a2.
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Find the center, transverse axis, vertices, foci,
and asymptotes of
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Center (h, k) (-2, 4)
Transverse axis parallel to x-axis.
Vertices (h a, k) (-2 2, 4) or (-4, 4)
and (0, 4)
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(h, k) (-2, 4)
Asymptotes
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y - 4 2(x 2)
y - 4 -2(x 2)
(-2, 8)
V (-4, 4)
V (0, 4)
F (2.47, 4)
F (-6.47, 4)
C(-2,4)
(-2, 0)