Question

Find the equations of lines passes through point $(3,4)$ and parallel to axis. Also find the equation of lines parallel to these lines and at a distance of $8$ units.

Answer 1

Let lines $mn$ and $m^{{}^{\prime }}{n}^{{}^{\prime }}$ are situated at a distance of $8$ units from $AB$.
Then equation of line $mn$
$y=12$ and $y=-4$ or $y+4=0$
Let lines $rs$ and $r^{{}^{\prime }}{s}^{{}^{\prime }}$ are located at a distance of $8$ unit from line $PQ$
The equations of line $rs$ and $r^{{}^{\prime }}{s}^{{}^{\prime }}$
$x=-11$
and $x=-5$
or $x+5=0$