The line parallel to $x$-axis and passing through the point of intersection of lines $a x+2 b y+3 b=0$ and…
The line parallel to $x$-axis and passing through the point of intersection of lines $a x+2 b y+3 b=0$ and $b x-2 a y-3 a=0$, where $(a, b) \neq(0,0)$ is
above $x$-axis at a distance $2 / 3$ from it
above $x$-axis at a distance $3 / 2$ from it
below $x$-axis at a distance $3 / 2$ from it
below $x$-axis at a distance $2 / 3$ from it
Solution
Given lines are
$
a x+2 b y+3 b=0 \text { and }
$
$
b x-2 a y-3 a=0
$
Since, required line is $\|$ to $x$-axis
$
\therefore x=0
$
We put $x=0$ in given equation, we get
$
2 b y=-3 b \Rightarrow y=-\frac{3}{2}
$
This shows that the required line is below $x$-axis at a distance of $\frac{3}{2}$ from it