How do you write a standard form equation for the hyperbola with vertices at (-2, 0) and (2, 0) and foci at (-6, 0) and (6, 0)?
Because the vertices are horizontal, we know that the standard form is,
, the vertices are
and the foci are
Using the form of the vertices and the given vertices we can write the following equations:
Solving the first two equations we have:
Using the form of the foci and one of the given foci we can write:
Substitute in the known values for h and a:
Solve for b:
Substituting the know values into equation :
Equation  is the answer.