Hyperbolas
Hyperbolas
Example 2
Graph the following hyperbola. Find its center, vertices, foci, and the equations of its asymptote lines.
![HyperbolasEx2-1 HyperbolasEx2-1](https://claregladwinresd.glk12.org/pluginfile.php/974/mod_book/chapter/449/Conic_Sections/images/HyperbolasEx2-1.png)
Vertices: (0, 2), (0, -2)
Foci: (0, ?13), (0, -?13)
Equations of asymptote lines:![HyperbolasEx2-3 HyperbolasEx2-3](https://claregladwinresd.glk12.org/pluginfile.php/974/mod_book/chapter/449/Conic_Sections/images/HyperbolasEx2-3.png)
![HyperbolasEx2-1 HyperbolasEx2-1](https://claregladwinresd.glk12.org/pluginfile.php/974/mod_book/chapter/449/Conic_Sections/images/HyperbolasEx2-1.png)
Step 1 . Identify the center, vertices, foci, and the equations of asymptotes.
This is a hyperbola with center at (0, 0), and its transverse axis is along the y-axis.
![HyperbolasEx2-2 HyperbolasEx2-2](https://claregladwinresd.glk12.org/pluginfile.php/974/mod_book/chapter/449/Conic_Sections/images/HyperbolasEx2-2.png)
Vertices: (0, 2), (0, -2)
Foci: (0, ?13), (0, -?13)
Equations of asymptote lines:
![HyperbolasEx2-3 HyperbolasEx2-3](https://claregladwinresd.glk12.org/pluginfile.php/974/mod_book/chapter/449/Conic_Sections/images/HyperbolasEx2-3.png)
Step 2 . Graph the conic.
![HyperbolasEx2-4 HyperbolasEx2-4](https://claregladwinresd.glk12.org/pluginfile.php/974/mod_book/chapter/449/Conic_Sections/images/HyperbolasEx2-4.png)