The distance between the pair of lines \(x^2+2 \sqrt{2} x y+2 y^2+4 x+4 \sqrt{2} y+1=0\), is
The distance between the pair of lines \(x^2+2 \sqrt{2} x y+2 y^2+4 x+4 \sqrt{2} y+1=0\), is
\(4 \sqrt{2}\)
\(2 \sqrt{2}\)
2
\(6 \sqrt{2}\)
Solution
Given, equation of pair of lines is
\(x^2+2 \sqrt{2} x y+2 y^2+4 x+4 \sqrt{2} y+1=0\)
The distance between the pair of lines \(a x^2+2 h x y+b y^2+2 g x+2 f y+c=0\) is given by
\(d=2 \sqrt{\frac{g^2-a c}{a(a+b)}}\)
Here,
\(a=1, b=2, c=1, g=2\)
\(\therefore\) Required distance \(=2 \sqrt{\frac{4-1}{1(1+2)}}=2 \sqrt{\frac{3}{3}}=2\)