Question

Sol. [Key Concept: Image of a pair of lines in the mirror $y = 0$: replace $y \rightarrow - y$, so the sign of the $xy$-term flips.]

$$ax^{2} + by^{2} + 2hxy = 0$$

Put $x = X,y = - Y$, in the equation of pair $L_{1}$ and $L_{2}$.

$$\Rightarrow aX^{2} + b( - Y)^{2} + 2h(X)( - Y) = 0 $$$\Rightarrow aX^{2} + bY^{2} - 2hXY = 0$ is the required equation.