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Your Notes<br />
Example 2 Write an equation of a hyperbola<br />
Write an equation of the<br />
y<br />
hyperbola with foci at<br />
(25, 0) and (5, 0) and<br />
(−4, 0) (4, 0)<br />
vertices at (24, 0) and<br />
(−5, 0)<br />
2<br />
(5, 0)<br />
(4, 0).<br />
The foci and vertices lie on the<br />
-axis equidistant from the<br />
origin, so the transverse axis is<br />
6 x<br />
and the center is the origin. The foci are<br />
each units from the center, so c 5 . The vertices<br />
are each units from the center, so a 5 .<br />
Because c2 5 a2 1 b2 , you have b2 5 c2 2 a2 . Find b2 .<br />
b2 5 c2 2 a2 5 5<br />
Because the transverse axis is horizontal, the standard<br />
form of the equation is as follows:<br />
5 1 Substitute 4 for a and 9 for b 2 .<br />
5 1 Simplify.<br />
Checkpoint Write an equation of the hyperbola with<br />
the given foci and vertices.<br />
2. Foci: (0, 28), (0, 8)<br />
Vertices: (0, 25), (0, 5)<br />
246 Lesson 9.5 Algebra 2 Notetaking Guide Copyright © Holt McDougal. All rights reserved.
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