Question 572346
Here's how I go about it:
{{{ 9x^2-4y^2+18x+32y-91=0 }}} --> {{{(9x^2+18x)+(-4y^2+32y)-91=0}}} --> {{{9(x^2+2x)+(-4)(y^2-8y)-91=0}}} --> {{{9((x^2+2x+1)-1)-4((y^2-8y+16)-16)-91=0}}} --> {{{9((x+1)^2-1)-4((y-4)^2-16)-91=0}}} --> {{{9(x+1)^2-9-4(y-4)^2-4(-16)-91=0}}} --> {{{9(x+1)^2-4(y-4)^2-9+64-91=0}}} --> {{{9(x+1)^2-4(y-4)^2-36=0}}} --> {{{9(x+1)^2-4(y-4)^2=36}}}
and dividing both sides by 36
{{{(x+1)^2/4-(y-4)^2/9=1}}}