Question

Let $a$ be the distance between line $−x+y=2$ and $x−y=2$ and $β$ be the distance between the lines $4x−3y=5$ and $6y−8x=1,$ then

• A. $20\sqrt{2}β=11Î\pm$
• B. $20\sqrt{2}Î\pm =11β$
• C. $11\sqrt{2}β=20Î\pm$
• D. None of these

Answer 1

Answer: (A)

Given $Î\pm$ be the distance between lines
$x−y+2=0$ and $x−y−2=0$.
$∴Î\pm =\frac{âˆ\pounds 2+2âˆ\pounds }{\sqrt{1+1}}=\frac{âˆ\pounds 4âˆ\pounds }{\sqrt{2}}=2\sqrt{2}$
and $β$ be the distance between the lines
$4x−3y−5=0$ and $4x−3y+1/2=0$
$∴β=\frac{âˆ\pounds 5+\frac{1}{2}âˆ\pounds }{\sqrt{(4{)}^2+(3{)}^2}}$
$=\frac{âˆ\pounds 11âˆ\pounds }{2\sqrt{25}}=\frac{11}{10}$
Now, $\frac{Î\pm }{β}=\frac{2\sqrt{2}}{11/10}$
$⇒\frac{Î\pm }{β}=\frac{20\sqrt{2}}{11}$
$⇒20\sqrt{2}β=11Î\pm$