Question 896452
{{{16y^2-4x^2-36x-24y-36=0}}}
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{{{4y^2-x^2-9x-8y-9=0}}}
{{{4y^2-8y-x^2-9x=9}}}
{{{4(y^2-2y)-(x^2+9x)=0}}}
{{{Complete The Squares}}}
{{{4(y^2-2y+1)-(x^2+9x+(9/2)^2)=9+4-81/4}}}
{{{4(y-1)^2-(x+9/2)^2=13-81/4}}}
{{{4(y-1)^2-(x+9/2)^2=52/4-81/4}}}
{{{4(y-1)^2-(x+9/2)^2=-29/4}}}

{{{-(16/29)(y-1)^2+(4/29)(x+9/2)^2=1}}}

{{{highlight_green((x+9/2)^2/(29/4)-(y-1)^2/(29/16)=1)}}}


ASYMPTOTES


{{{highlight(y=-(sqrt(29/16)/sqrt(29/4))(x+9/2)+1)}}}
and
{{{highlight(y=(sqrt(29/16)/sqrt(29/4))(x+9/2)+1)}}}


These still need simplification in order to be finished.



Refer to your textbook to see how to obtain formula for the asymptotes, or refer to
other favorite reference source.