How do you write an equation for a hyperbola with vertices (1, 3) and (-5, 3), and foci (3, 3) and (-7, 3)?
The equation is:
Please notice that the vertices are of the forms:
The same information can be deduced from the foci, which have the forms:
The standard form for the equation of a hyperbola, where the vertices and foci have these properties, is the horizontal transverse axis form:
Compute h and a:
To complete the equation, we only need the value of b but, to find the value of b, we must, first, find the value of c:
Solve for b, using the equation