Math 25 Trigonometry December 1, 1999

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Math 25 --- Trigonometry December 1, 1999

• Section 6.3 questions
• Section 6.4
• Break
• Section 6.6
• Assignments 29 and 30

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AnnouncementsDecember 1, 1999

• Trig Notebooks due December 3 by 2pm.
• Final Wednesday December 15

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Definition of an Ellipse
An ellipse is the collection of all points
P(x,y) in the plane the sum of whose distance
from two fixed points, called the foci, is a
constant.
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Equations of an Ellipse
Center at
Horizontal Major Axis
Vertices
Foci
Vertical Major Axis
Vertices
Focus
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Definition of a Hyperbola
A hyperbola is the collection of all points
P(x,y) in the plane the difference of whose
distance from two fixed points, called the foci,
is a constant.
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Equations of a Hyperbola
Center at
Horizontal Transverse Axis (opens left/right)
Vertices
Foci
Vertical Transverse Axis (opens up/down)
Vertices
Focus
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Asymptotes of a Hyperbola
Center at
Horizontal Transverse Axis (opens left/right)
Vertical Transverse Axis (opens up/down)
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Equations of a Hyperbola
Center at
Horizontal Transverse Axis (opens left/right)
Vertices
Foci
Vertical Transverse Axis (opens up/down)
Vertices
Focus
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Asymptotes of a Hyperbola
Center at
Horizontal Transverse Axis (opens left/right)
Vertical Transverse Axis (opens up/down)
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Definition of a Conic
Let D denote a fixed line called the directrix
let F denote a fixed point called the focus,
which is not on D and let e be a fixed positive
number called the eccentricity. A conic is the
set of points P in the plane such that the ratio
of the distance from F to P to the distance from
P to D equals e. That is the set of points P for
which
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Properties of a Conic
If e1, the conic is a parabola. If elt1, the
conic is an ellipse. If egt1, the conic is a
hyperbola.
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Polar Equations of Conics
Focus at the Pole and Eccentricity, e
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Assignment 29 and 30

• Homework 6.4 pbs 5-50 (every 5th), 61
• Homework 6.6 5-35 (every 5th), 37