Let $p_1, p_2, p_3$ be the perpendicular distance between pair of parallel lines represented by $x^2-3x-4=0,$  $y^2-5y+6=0,4x^2+20xy+25y^2=0$

$x^2-3x-4=0\Rightarrow x_1+x_2=\frac{-b}{a}=3$ and 

$x_1{x}_2=\frac{c}{a}=-4\Rightarrow p_1=\left|x_1-x_2\right|=\sqrt{{\left(x_1+x_2\right)}^2-4x_1{x}_2}=5$

$y^2-5y+6=0\Rightarrow y_1+y_2=5,y_1{y}_2=6$

$\Rightarrow p_2=\left|y_1-y_2\right|=\sqrt{25-24}=1$

and $4x^2+20xy+25y^2=0$

$\Rightarrow (2x+5y{)}^2=0$

Lines are coincident ${\perp }^{\text{lar }}$distance $\left(p_3\right)=0$