If lx + ly + p = 0 and lx + ly - r = 0 are two parallel lines, then distance between them is equal to |(m/n)|, where m and n respectively are

Question

If lx + ly + p = 0 and lx + ly - r = 0 are two parallel lines, then distance between them is equal to |(m/n)|, where m and n respectively are (A) p-r, √2l (B) r-p, √2l (C) p+r, √2l (D) p+r, √2l

Tardigrade Admin · Accepted Answer

Given, lines lx+ly+p=0 and lx+ly-r=0 are parallel. ∴ Distance between two parallel lines =|(p-(-r)/√(l)2+(l)2)|=|(p+r/√2l2)| =|(p+r/√2l)|

Q. If $l x + l y + p = 0$ and $l x + l y - r = 0$ are two parallel lines, then distance between them is equal to $∣ ∣ \frac{m}{n} ∣ ∣$ , where $m$ and $n$ respectively are

$p - r$ , $2 l$

$r - p$ , $2 l$

$p + r$ , $2 l$

$p + r$ , $2 l$

Given, lines $l x + l y + p = 0$ and $l x + l y - r = 0$ are parallel.
$∴$ Distance between two parallel lines
$= ∣ ∣ \frac{p - ( - r )}{( l ) ^{2} + ( l ) ^{2}} ∣ ∣ = ∣ ∣ \frac{p + r}{2 l ^{2}} ∣ ∣$
$= ∣ ∣ \frac{p + r}{2 l} ∣ ∣$

Q. If lx+ly+p=0 and lx+ly−r=0 are two parallel lines, then distance between them is equal to ∣∣​nm​∣∣​, where m and n respectively are

p−r, 2​l

r−p, 2l​

p+r, 2l​

p+r, 2​l

Given, lines lx+ly+p=0 and lx+ly−r=0 are parallel. ∴ Distance between two parallel lines =∣∣​(l)2+(l)2​p−(−r)​∣∣​=∣∣​2l2​p+r​∣∣​ =∣∣​2​lp+r​∣∣​

Q. If $l x + l y + p = 0$ and $l x + l y - r = 0$ are two parallel lines, then distance between them is equal to $∣ ∣ \frac{m}{n} ∣ ∣$ , where $m$ and $n$ respectively are

$p - r$ , $2 l$

$r - p$ , $2 l$

$p + r$ , $2 l$

$p + r$ , $2 l$

Given, lines $l x + l y + p = 0$ and $l x + l y - r = 0$ are parallel.
$∴$ Distance between two parallel lines
$= ∣ ∣ \frac{p - ( - r )}{( l ) ^{2} + ( l ) ^{2}} ∣ ∣ = ∣ ∣ \frac{p + r}{2 l ^{2}} ∣ ∣$
$= ∣ ∣ \frac{p + r}{2 l} ∣ ∣$