write an equation for the hyperbola:
vertices (-7,0) and (7,0), conjugate axis of length 10.

The hyperbola has its center at the origin because the
center is halfway between the vertices and the origin
is halfway between the vertices.

The equation of a hyperbola which opens right and left is

     

where a = half the length of the transverse axis
(the transverse axis is the line between the vertices)

and

b = half the length of the conjugate axis
(the conjugate axis is a line perpendicular to the
transverse axis at the center, half of which is 
above the center and half below.

So since the vertices are (-7,0) and (7,0) the major
axis is 14 and half that is 7, so a = 7

Half the conjugate axis is half of 10, or 5.  So b = 5.

So the equation is:

     

or

       

If you want to see it graphed with the defining
rectangle and asymptotes, post again.

Edwin