Question 1090308
{{{x^2-9y^2+4x-36y-41=0}}} => this is a hyperbola


{{{(x-h)^2/a^2-(y-k)^2/b^2=1}}}


rearrange terms and complete squares:


{{{x^2+4x-9y^2-36y-41=0}}}


{{{(x^2+4x+b^2)-b^2-9(y^2+4y+b^2)-9b^2=41}}}


{{{(x^2+4x+2^2)-2^2-9(y^2+4y+2^2)-9*2^2=41}}}


{{{(x+2)^2-4-9(y+2)^2-9*4=41}}}


{{{(x+2)^2-9(y+2)^2-36-4=41}}}


{{{(x+2)^2-9(y+2)^2-40=41}}}


{{{(x+2)^2-9(y+2)^2=41+40}}}


{{{(x+2)^2-9(y+2)^2=81}}}


{{{(x+2)^2/81-9(y+2)^2/81=81/81}}}


{{{(x+2)^2/81-cross(9)(y+2)^2/cross(81)9=1}}}


{{{(x+2)^2/81-(y+2)^2/9=1}}}


{{{(x+2)^2/9^2-(y+2)^2/3^2=1}}}

=>{{{h=-2}}}, {{{k=-2}}},{{{a=9}}}, {{{b=3}}}

center at ({{{-2}}},{{{-2}}})

{{{drawing( 600, 600, -15, 15, -15, 15,
circle(-2,-2,.12), locate(-2,-2,C(-2,-2)),
 graph( 600, 600, -15, 15, -15, 15,(1/3)(-sqrt(x^2 + 4x - 5) -6),(1/3) (sqrt(x^2 + 4x - 5)-6))) }}}