Equation to the pair of lines passing through the origin whose sum and product of slopes are A.M. and G.M. of 4 and 16 is

$\begin{array}{l}Lety=m_{1}xandy=m_{2}xarelines\\ sumofslopes=A.Mof4and16\\ \Rightarrow m_1+m_2=\frac{4+16}{2}=10\\ productofslopes=G.Mof4and16\\ m_1{m}_2=\sqrt{4\times 16}\Rightarrow 8\\ ThecombinedEquation(m_{1}x-y)(m_{2}y-y)=0\\ \Rightarrow m_1{m}_2{x}^2-(m_1+m_2)xy-y^2=0\\ \Rightarrow 8x^2-10xy+y^2=0\end{array}$