The two lines $4x^2-24xy+11y^2=0$ makes with x-axis angles such that difference of their tangents is

 Given Equation $4x^2-24xy+11y^2=0$

Comparing with  $a{x}^2+2hxy+b{y}^2=0$

$a=4,2h=-24\Rightarrow h=-12,b=11$

$\begin{array}{l}\therefore Let{m}_1,m_{2}areslopesofthelines\\ \therefore m_1-m_2=\frac{2\sqrt{h^{2}as}}{\left|b\right|}=\frac{2\sqrt{144-44}}{11}=\frac{20}{11}\end{array}$