Question

For a hyperbola, the foci lie on a line called the _______________

Short answer

For a hyperbola, the foci lie on a line called the Transverse axis.

Step-by-step solution

Step 1. Concept

A Hyperbola is the collection of all points in the plane, the difference of whose

distances from two fixed points, called the foci, is a constant.

The above figure is the graph of the hyperbola$\frac{x^2}{9}-\frac{y^2}{16}=1$with focii at $(5,0)$and $(-5,0)$.

The line containing the foci is called the Transverse axis.

Here the foci lie on the $x-$axis . Hence here the transverse axis is the$x-$axis.

Step 2. Conclusion

For a hyperbola, the foci lie on a line called the Transverse axis.