Question 27827
{{{(4x^2-8x)-25y^2-96=0}}}
{{{4(x^2-2x)-25(y^2)-96+0}}} ---> complete the square
{{{4(x^2-2x+1-1)-25(y^2)-96+0}}}
{{{4((x-1)^2-1)-25(y^2)-96=0}}}
{{{4(x-1)^2-4-25(y^2)-96=0}}}
{{{4(x-1)^2-25(y^2)-100=0}}}
{{{4(x-1)^2-25(y^2)=100}}}
{{{(x-1)^2/25-y^2/4=1}}}



Center at (1,0) 
Foci (c)=4+25=29
{{{c=sqrt(29)}}}


Foci of hyperbola at {{{c=sqrt(29+1,0)}}} and {{{c=sqrt(-29)+1,0}}}

{{{a^2=25}}}
a=5
Vertices
(5+1,0) and (-5+1,0)
Sorry I do not know about the slope and how to graph it here.


Paul.