# How do you identify the vertices, foci, and direction of #(x-3)^2/4-(y+1)^2/9=1#?

##### 1 Answer

The direction is horizontal transverse

The vertices are at

The foci are

#### Explanation:

Please notice that the center of the hyperbola is

To find the vertices, force the negative term to become zero by setting

We are about to take the square root of both sides so we need to write two equation one where the right side is 2 and the other where the right side is -2:

The vertices are at

We know that the y coordinate of both foci is -1 but the x coordinate is plus or minus the distance c from the x coordinate of the center, 3 The formula for c is:

The foci are