The equation ${\mathrm{x}}^2{\mathrm{y}}^2-2{\mathrm{xy}}^2-3{\mathrm{y}}^2-4{\mathrm{x}}^2\mathrm{y}+8\mathrm{xy}+12\mathrm{y}=0$ represent 

both pair have same angular bisectors. Angular bisectors of 2nd pair are $\frac{{\mathrm{x}}^2-{\mathrm{y}}^2}{(\mathrm{a}+\mathrm{\lambda })-(\mathrm{b}+\mathrm{\lambda })}=\frac{\mathrm{xy}}{\mathrm{h}}$
$\Rightarrow \frac{{\mathrm{x}}^2-{\mathrm{y}}^2}{\mathrm{a}-\mathrm{b}}=\frac{\mathrm{xy}}{\mathrm{h}}$ which are angular bisector of pair $\text{ (1) }\therefore \mathrm{\lambda }\in \mathrm{R}$