Hyperbolas
Hyperbolas
Hyperbolas
Transverse Axis
x-axis
A hyperbola centered at (0, 0) whose transverse axis is along the x-axis has the following equation in standard form.
Vertices: (a, 0) and (-a, 0)
Foci: (c, 0) and (-c, 0), where c2 = a2 + b2
Equation of asymptote lines:
![TransverseX2 TransverseX2](https://claregladwinresd.glk12.org/pluginfile.php/974/mod_book/chapter/446/Conic_Sections/images/TransverseX2.png)
y-axis
A hyperbola centered at (0, 0) whose transverse axis is along the y-axis has the following equation in standard form.
![TransverseY1 TransverseY1](https://claregladwinresd.glk12.org/pluginfile.php/974/mod_book/chapter/446/Conic_Sections/images/TransverseY1.png)
In general, when a hyperbola is written in standard form, the transverse axis is along, or parallel to, the axis of the variable that is not being subtracted.
![TransverseY1 TransverseY1](https://claregladwinresd.glk12.org/pluginfile.php/974/mod_book/chapter/446/Conic_Sections/images/TransverseY1.png)
Vertices: (0, a) and (0, -a)
Foci: (0, c) and (0, -c), where c2 = a2 + b2
Equation of asymptote lines:
Foci: (0, c) and (0, -c), where c2 = a2 + b2
Equation of asymptote lines:
![TransverseY2 TransverseY2](https://claregladwinresd.glk12.org/pluginfile.php/974/mod_book/chapter/446/Conic_Sections/images/TransverseY2.png)
In general, when a hyperbola is written in standard form, the transverse axis is along, or parallel to, the axis of the variable that is not being subtracted.