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Example 1 Graph an equation of a hyperbola
Graph 36y 2 2 9x 2 5 324. Identify the vertices, foci,
and asymptotes of the hyperbola.
Solution
1. Rewrite the equation in standard
form.
5 1
2. Identify the vertices, foci, and
asymptotes. Note that a2 5
and b2 5 , so a 5 and b 5 . The y2-term is , so the transverse axis is and
the vertices are (0, 6 ). Find the foci.
c2 5 a2 1 b2 5 5 , so c 5 Ï }
The foci are at (0, 6 Ï }
) ø (0, 66.7).
The asymptotes are y 5 6
a
} x, or y 5
b
.
3. Draw the hyperbola. Draw a rectangle centered at the
origin that is 2a 5 units high and 2b 5 units
wide. The asymptotes pass through opposite corners
of the rectangle. Then, draw the hyperbola passing
through the vertices and approaching the asymptotes.
Checkpoint Graph the equation. Identify the vertices,
foci, and asymptotes of the hyperbola.
1. x2
}
49
2 y2
}
9 5 1
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