Question

If the equation $2xy+4x-6y+k=0$ represents a pair of straight lines, then the value of $(k+20)$ is

Answer 1

The general equation of second degree :
$a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$
Given : $2xy+4x-6y+k=0$
Comparing both,
$a=0,b=0,h=1,g=2,f=-3,c=k$
For two straight lines,
$h^2-ab\ge 0$ and $△=0$
$△=0+2(-3)\left(2\right)\left(1\right)-0-0-k(1{)}^2=-12-k$
$\Rightarrow -12-k=0$
$\Rightarrow k=-12$
$\therefore k+20=-12+20=8$