Two point charges  $Qand{Q}_0$ are placed at some distance. One of the electric field lines due to this charge configuration is shown in fig. Find the value of $\left|\frac{Q_0}{Q}\right|$

Let the charge Q at (0, 0) be positive and charge $Q_0$  at (0, 0) be negative 
$\Rightarrow$ electric field at P(3, 4) is in horizontal direction 
 So vertical component of electric field at P is zero

 Distance of the point P from origin is is $\sqrt{3^2+4^2}=5 \mathrm{unit} \mathrm{and} \mathrm{from} {\mathrm{Q}}_0 \mathrm{it} \mathrm{is} \sqrt{7^2+4^2}=65 \mathrm{unit}$

But at P vertical component due to Q and Q₀ are equal and opposite 

Vertical component

$\frac{K Q}{25}\sin {\theta }_1 and\frac{ K{Q}_0}{65}\sin {\theta }_2$

$\frac{KQ}{25}\frac{4}{5}=\frac{K{Q}_0}{65}\frac{4}{\sqrt{65}}$

$\frac{Q_0}{Q}=\frac{13\sqrt{65}}{25}$