3.7.12
Monday, March 05, 2012
6:57 PM
9-5 Hyperbolas
Vocabulary:
• Hyperbola: the set of all points P in the plane such that the difference between the
distances from P to two fixed points is a given constant
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Each fixed point is a focus, and the distances
and
are the focal radii.
The center of a hyperbola is the midpoint of the line segment joining its foci.
To find an equation of the hyperbola having foci
of focal radii 6:
and
and a difference
or
Remember that
is the distance from point P (x, y) to point
Equations of hyperbola:
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(-5, 0)
If the
term is positive, the line containing the center and foci is horizontal.
If the
term is positive, the line containing the center and foci is vertical.
The denominator of the positive squared term is
The difference of focal radii is
.
.
Examples:
Determine the intercepts, asymptotes, foci, and sketch the graph:
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Find an equation of the hyperbola having foci (0, 3) and (0, -3) and difference of focal radii
equal to 2.
Find an equation of the hyperbola with asymptotes
and foci (0, 3) and (0, -3).
Practice:
Determine the intercepts, asymptotes and foci
Sketch the graph of
Find an equation of the hyperbola with foci (0, 13) and (0, -13) and with 24 as the
difference of the focal radii
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Homework: p. 430 #7-35 odd
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