 # Hyperbola: Transverse Axis How to find the transverse of a hyperbola: definition, formulas, examples, and their solutions.

## Definition A hyperbola is the set of points
whose difference of the distances from the foci
is constant.

Hyperbola - Proof of the formula x2/a2 - y2/b2 = 1

## Formula: Transverse Axis of x2/a2 - y2/b2 = 1 For the hyperbola x2/a2 - y2/b2 = 1,

the x2 term is (+).

Then the vertices are (±a, 0).

So the transverse axis (= distance between the vertices)
is 2a.

## Example 1: Transverse Axis of x2/9 - y2/16 = 1 Change the equation in standard form.

9 = 32
16 = 42

So x2/32 - y2/42 = 1.

The x2 term is (+).

So the transverse axis is 2⋅3.

2⋅3 = 6

So (transverse axis) = 6.

This is the graph of x2/32 - y2/42 = 1.

The x2 term is (+).

So the transverse axis is 6.

And the it is parallel to the x-axis.

## Formula: Transverse Axis of y2/b2 - x2/a2 = 1 For the hyperbola y2/b2 - x2/a2 = 1,

the y2 term is (+).

Then the vertices are (0, ±b, 0).

So the transverse axis (= distance between the vertices)
is 2b.

## Example 2: Transverse Axis of x2 - y2 = -4 Change the equation in standard form.

Divide both sides by -4.

Switch the order of the terms in the left side.

4 = 22

So y2/22 - x2/22 = 1.

The y2 term is (+).

So the transverse axis is 2⋅2.

2⋅2 = 4

So (transverse axis) = 4.

This is the graph of y2/22 - x2/22 = 1.

The y2 term is (+).

So the transverse axis is 4.

And it is parallel to the y-axis.