To determine the length of the transverse axis of a hyperbola, you first need to know its standard form. For a hyperbola centered at the origin, the standard forms are:
- \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) for horizontal hyperbolas, where the transverse axis is along the x-axis.
- \( \frac{y^2}{a^2} - \frac{x^2}{b^2} = 1 \) for vertical hyperbolas, where the transverse axis is along the y-axis.
In both cases, the length of the transverse axis is given by \(2a\), where \(a\) is the distance from the center to each vertex along the transverse axis.
To answer your question:
The expression that gives the length of the transverse axis of the hyperbola is \(2a\).