# How do you find the standard form of the hyperbola that satisfies the given conditions: Vertices at #(0, +-2)#, foci at #(0, +-4)#?

##### 1 Answer

#### Answer:

Please see the explanation for steps leading to the equation:

#### Explanation:

The y coordinate of the vertices is the one that changes, therefore, the hyperbola is the vertical transverse axis type. The general equation for this type is:

where:

The centerpoint is

The vertices are:

And the foci are:

Given that the vertices are

Use equations [2] and [3] to solve for a and k:

Given that one of foci is

Substitute 0 for k and 2 for a:

Solve for b:

Substitute all of the computed values into the general form: