# How do you find the equation of the hyperbola with center at the origin and vertices #(+-1,0)# and asymptotes #y=+-3x#?

##### 1 Answer

Please see the explanation.

#### Explanation:

Please observe that the vertices are horizontally oriented,

where h and k are the center point

We are given that the center is the origin so substitute 0 for h and k into equation [1]:

We can see that the distance from the center to either vertex is 1, therefore substitute 1 for a into equation [2]:

We are given that the slope of the vertices is

Substitute 1 for a:

To substitute 3 for b into equation [3]:

You can simplify equation [4] if you like, but I recommend that you leave it in this form.