If a: b: c = 1: 2: 3 then the lines represented by $a{x}^2+bxy+c{y}^2=0$ are

            

a: b: c=1 : 2 : 3 

a=k, b=2k, c=3k

The equation 

$\begin{array}{l}a{x}^2+bxy+c{y}^2=0\\ x^2+2xy+3y^2=0\end{array}$

Comparing with 

$\begin{array}{l}a{x}^2+2bxy+b{y}^2=0\\ \Rightarrow a=1h=1b=3\\ \Rightarrow h^2=1,ab=3\\ h^2<ab\end{array}$

The lines are coincident