Question

The distance between the pair of lines represented by $x^{2}+2 \sqrt{2} x y+2 y^{2}+4 x+4 \sqrt{2} y+1=0$, is

• A. 1
• B. 2
• C. $\sqrt{2}$
• D. 4

Answer 1

Answer: (B)

Given,
$x^{2}+2 \sqrt{2} x y+2 y^{2}+4 x+4 \sqrt{2} y+1=0$
We know that,
The distance ' $d$ ' between the pair of straight lines represented by
$a x^{2}+2 h x y+b y^{2}+2 g x+2 f y+c=0$ is given by
$d=2 \sqrt{\frac{g^{2}-a c}{a(a+b)}}$
Here, $a=1, \,b=2,\, c=1,\, g=2$
$\therefore d=2 \sqrt{\frac{4-1}{1(1+2)}}=2 \sqrt{\frac{3}{3}}=2$