3.8.13
9.5 Hyperbolas
Tuesday, July 17, 2012
10:28 PM
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
Each fixed point is a focus, and the distances
radii.
and
are the focal
The center of a hyperbola is the midpoint of the line segment joining its foci.
• Asymptote: the imaginary line a graph approaches but never touches
To find an equation of the hyperbola having foci
difference of focal radii 6:
and
and a
or
Remember that
is the distance from point P (x, y) to point
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(-5, 0)
Equations of hyperbola:
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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Determine the intercepts, asymptotes, foci, and sketch the graph:
10
9
8
y
7
6
5
4
3
2
1
-1 0 -9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
x
1 2 3 4 5 6 7
8 9 10
-8
-9
-1 0
10
9
8
y
7
6
5
4
3
2
1
-1 0 -9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
-9
-1 0
Find an equation of the hyperbola having foci (0, 3) and (0, -3) and
difference of focal radii equal to 2.
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x
1 2 3 4 5 6 7
8 9 10
Find an equation of the hyperbola with asymptotes
(0, -3).
Practice:
Determine the intercepts, asymptotes and foci
Sketch the graph of
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and foci (0, 3) and
Find an equation of the hyperbola with foci (0, 13) and (0, -13) and with 24 as the
difference of the focal radii
In Class: p. 430 #7-35 odd
Homework: MathXL 9.5 HW
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