Question

Find the equation. of the straight line equidistant from the straight lines 4x +3y+10=0 and 4x +3y+2=0.

Answer 1

Let the line equidistant from these lines be $y=-\frac{4}{2}x+c$

Distance between $4x+3y+10=0$ and $4x+3y+2=0$

$=>D_1=\left|\frac{\frac{-10}{3}+\frac{2}{3}}{\sqrt{1+\frac{16}{9}}}\right|=\left|\frac{\frac{-8}{3}}{\frac{5}{3}}\right|=\frac{8}{5}$

Distance between new line and first one line=>$\frac{D_1}{2}=\frac{1}{2}\left(\frac{8}{5}\right)=>\frac{4}{5}\left|\frac{c+\frac{10}{3}}{\sqrt{1+\frac{16}{9}}}\right|=>4=3c+10=>c=-2$

line equidistant from these lines is $3y+4x+6=0$