How do you find the equation of the hyperbola with center at the origin and vertices #(+-1,0)# and asymptotes #y=+-3x#?
Please see the 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 :
We can see that the distance from the center to either vertex is 1, therefore substitute 1 for a into equation :
We are given that the slope of the vertices is
Substitute 1 for a:
To substitute 3 for b into equation :
You can simplify equation  if you like, but I recommend that you leave it in this form.