If the pair of lines $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ intersect on y-axis, then 2fgh=

Given pair of lines intersect on y-axis $\Rightarrow f^2=bc$

$$\begin{gathered} abc+2fgh-a{f}^2-b{g}^2-c{h}^2=0 \\ sub f^2=bc then we get \\ \Rightarrow 2fgh=b{g}^2+c{h}^2. \end{gathered}$$