Two mutually perpendicular wire carry charge densities ${\lambda }_1$ and ${\lambda }_2$. The electric line of force makes angle $\alpha$ with second wire, then the ratio $\frac{{\lambda }_1}{{\lambda }_2}$ is equal to (in terms of angle $\alpha )$

Q. Two mutually perpendicular infinite wires carry positive charge densities ${\lambda }_1$ and ${\lambda }_2$. The electric lines of force makes angle $\alpha$ with second wire then $\frac{{\lambda }_1}{{\lambda }_2}$ is

Q.
Two mutually perpendicular infinite wires along $x$-axis and $y$-axis carry charge densities ${\lambda }_1\text{and}{\lambda }_2$. The electric line on force at $P$ is along the line $y=\frac{1}{\sqrt{3}}x$, where $P$ is also a point lying on the same line, then find $\frac{{\lambda }_2}{{\lambda }_1}$.

Q. Two mutually perpendicular infinite wires along $\text{x-}$axis and $\text{y-}$axis carry charge density ${\lambda }_1$ and ${\lambda }_2$. The electric line of force at $\text{P}$ is along the line $y=\frac{x}{\sqrt{3}}$, where $\text{P}$ is also a point lying on the same line, then find $\frac{{\lambda }_1}{{\lambda }_2}$

Q. Two mutually perpendicular infinite wires along $x-$axis and $y-$ axis carry charge densities ${\lambda }_1$ and ${\lambda }_2$ respectively. The electric line of force at P is along the line $y=\frac{1}{\sqrt{3}}x$, where P is also a point living on the same line. Find ${\lambda }_2/{\lambda }_1$
Diagram

Q. If $\alpha ,\beta$ are the roots of $\lambda (x^2+x)+x+5=0$ and ${\lambda }_1,{\lambda }_2$ are two values of $\lambda$ for which $\alpha ,\beta$ are connected by the relation $\frac{\alpha }{\beta }+\frac{\beta }{\alpha }=4,$ then the value of $\frac{{\lambda }_1}{{\lambda }_2}+\frac{{\lambda }_2}{{\lambda }_1}$ is equal to