Hyperbolas
Hyperbolas
Center (h, k)
A hyperbola centered at (h, k) will have the following standard equations:
Foci: (h+c, k), (h-c, k), where c2 = a2 + b2
- If the transverse axis is horizontal, then
![HyperbolasCenter1-1 HyperbolasCenter1-1](https://claregladwinresd.glk12.org/pluginfile.php/974/mod_book/chapter/450/Conic_Sections/images/HyperbolasCenter1-1.png)
Vertices: (h+a, k), (h-a, k)
Foci: (h+c, k), (h-c, k), where c2 = a2 + b2
Equations of asymptote lines:
![HyperbolasCenter1-2 HyperbolasCenter1-2](https://claregladwinresd.glk12.org/pluginfile.php/974/mod_book/chapter/450/Conic_Sections/images/HyperbolasCenter1-2.png)
- If the transverse axis is vertical, then
![HyperbolasCenter2-3 HyperbolasCenter2-3](https://claregladwinresd.glk12.org/pluginfile.php/974/mod_book/chapter/450/Conic_Sections/images/HyperbolasCenter1-3.png)
Vertices: (h, k+a) and (h, k-a)
Foci: (h, k+c) and (h, k-c), where c2 = a2 + b2
Equations of asymptote lines:
![HyperbolasCenter1-4 HyperbolasCenter1-4](https://claregladwinresd.glk12.org/pluginfile.php/974/mod_book/chapter/450/Conic_Sections/images/HyperbolasCenter1-4.png)