NIMCET 2022 — Mathematics PYQ

Lines $-2x+y=2$ and $2x-y=2$ → $2x-y+2=0,2x-y-2=0$

$$<br>a=\frac{|2-(-2)|}{\sqrt{2^2+(-1{)}^2}}=\frac{4}{\sqrt{5}}<br>$$

Lines $4x-3y=5$ and $6y-8x=1$ → $8x-6y-10=0,8x-6y+1=0$

$$<br>b=\frac{|-10-1|}{\sqrt{8^2+(-6{)}^2}}=\frac{11}{10}<br>$$

Check relation:

$$<br>40b=44,11\sqrt{5}a=44<br>$$

$$<br>\boxed{40b=11\sqrt{5}a\text{(Option a)}}<br>$$