# How do you write an equation for the hyperbola with center (0,0), vertex (-2,0) and focus (4,0)?

##### 1 Answer

Please see the explanation.

#### Explanation:

The given, center, vertex, and focus share the same y coordinate, 0, ,therefore, the standard form for the equation of this type of hyperbola is the one corresponding to the Horizontal Transverse Axis type:

where

Substitute the center

We know that

Observing that the focus is a distance of 4 from the center we set

Substitute 4 for

Solve for b:

Substitute