Find the distance between the parallel straight lines $5\mathrm{x}-3\mathrm{y}-4=0,10\mathrm{x}-6\mathrm{y}-9=0$.

If ax + by +c₁ = 0 and ax + by + c₂ = 0 are two parallel lines then the  distance between two parallel lines is$\frac{\left|{\mathrm{c}}_2-{\mathrm{c}}_1\right|}{\sqrt{{\mathrm{a}}^2+{\mathrm{b}}^2}}$
Given lines
$\begin{array}{l}5\mathrm{x}-3\mathrm{y}-4=0\\ 10\mathrm{x}-6\mathrm{y}-8=0 ....\left(1\right)\end{array}$
$\text{ And }10\mathrm{x}-6\mathrm{y}-9=0 ...\left(2\right)$
$$\begin{gathered} \therefore \mathrm{eq}uations \left(1\right) \mathrm{and} \left(2\right) \mathrm{are} \mathrm{parallel} \\ \therefore \mathrm{The} \mathrm{distance} \mathrm{between} \left(1\right) \mathrm{and} \left(2\right) is \end{gathered}$$
$=\frac{|-8+9|}{\sqrt{100+36}}=\frac{1}{2\sqrt{34}}$