Question

The number of asymptotes of the curve given by $2xy+4x-6y+17=0$ is equal to

Answer 1

Given, $2xy+4x-6y+17=0$
Comparing with $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$
We get $a=0,b=0,c=17,g=2,h=1,f=-3$
Now, $\Delta =abc+2fgh-a{f}^2-b{g}^2-c{h}^2=-29\ne 0$
and $h^2-ab=1>0$
$\therefore$ Given equation represents a hyperbola and it will have two asymptotes.