Question 736705
{{{-9x^2+4y^2-54x+8y-113=0 }}}
rearrange terms
{{{-9x^2-54x+4y^2+8y-113=0 }}}
complete the square:
{{{-9(x^2+6x+9)+4(y^2+2y+1)=113-81+4 }}}
{{{-9(x+3)^2+4(y+1)^2=36}}}
rearrange terms:
{{{4(y+1)^2-9(x+3)^2=36}}}
divide by 36
{{{(y+1)^2/9-(x+3)^2/4=1}}}
This is an equation of a hyperbola with vertical transverse axis:
Its standard form: {{{(y-k)^2/a^2-(x-h)^2/b^2=1}}}, (h,k)=(x,y) coordinates of center.