How do you find the coordinates of the vertices, foci, and the equation of the asymptotes for the hyperbola #x^2-y^2=4#?
First, we need to have our equation in standard form:
That's better! To get to our answer, we need to know that our hyperbola is a horizontal hyperbola, which means that the vertices and foci will be have the same y-coordinate as the center.
Next, we need to know our the values of
In our case, the
To find our vertices and foci, we move out a certain amount of units in both directions:
Finally, let's get the equations of the hyperbola's asymptotes. The equations are