# How do you write the equation of the hyperbola given Foci: (0,-5),(0, 5) and vertices (0, -3), (0,3)?

##### 1 Answer

Please see the explanation for the process. The equation is

#### Explanation:

There are two types of hyperbolas, one where a line drawn through its vertices and foci is horizontal, and one where a line drawn through its vertices and foci is vertical. This hyperbola is the type where a line drawn through its vertices and foci is vertical. We know this by observing that it is the y coordinate that changes when we move from a focus point to a vertex.

The general equation for this type of hyperbola is:

Observe that the x coordinate of the foci and the vertices is 0; this tells us that

The value of k is the sum of y coordinate of the vertices divided by two:

Please notice that when

Let c = the distance between the the center point and focus = 5. The equation for the square of this distance helps us to find the value of b:

Simplifying a bit: