Question

A line parallel to $\frac{x}{5/3}+\frac{y}{5/4}=1$ has $x-$ intercept $2$ units and a line perpendicular to it has $y-$ intercept $2$ units. Then the absolute value of ratio of differences between $x-$ intercepts and $y-$ intercepts of perpendicular and parallel lines is

Answer 1

Given line is $3x+4y-5=0$
Therefore, line parallel to it is $y=-\frac{3}{4}x+c$
Given it has $x$ intercept is $2.$
$\Rightarrow c=\frac{3}{2}$
$\Rightarrow y$ intercept $=\frac{3}{2}$

Now, perpendicular line is $y=\frac{4}{3}x+2$ as $y-$ intercept is $2.$

$\therefore$ Ratio of differences between $x-$ intercepts to $y-$ intercepts of perpendicular lines and parallel line is
$\frac{|-\frac{3}{2}-2|}{|2-\frac{3}{2}|}=7$