Hyperbolas
Hyperbolas
Example 1
Graph the following hyperbola. Find its center, vertices, foci, and the equations of its asymptote lines.
![HyperbolasEx1-1 HyperbolasEx1-1](https://claregladwinresd.glk12.org/pluginfile.php/974/mod_book/chapter/448/Conic_Sections/images/HyperbolasEx1-1.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 x-axis.
![HyperbolasEx1-2 HyperbolasEx1-2](https://claregladwinresd.glk12.org/pluginfile.php/974/mod_book/chapter/448/Conic_Sections/images/HyperbolasEx1-2.png)
Vertices: (-4, 0), (4, 0)
Foci: (?41, 0), (-?41, 0)
Equations of asymptote lines:![HyperbolasEx1-3 HyperbolasEx1-3](https://claregladwinresd.glk12.org/pluginfile.php/974/mod_book/chapter/448/Conic_Sections/images/HyperbolasEx1-3.png)
Foci: (?41, 0), (-?41, 0)
Equations of asymptote lines:
![HyperbolasEx1-3 HyperbolasEx1-3](https://claregladwinresd.glk12.org/pluginfile.php/974/mod_book/chapter/448/Conic_Sections/images/HyperbolasEx1-3.png)
Step 2 . Graph the conic.
![HyperbolasEx1-4 HyperbolasEx1-4](https://claregladwinresd.glk12.org/pluginfile.php/974/mod_book/chapter/448/Conic_Sections/images/HyperbolasEx1-4.png)