The equation of second degree `x^2+2sqrt2x+2y^2+4x+4sqrt2y+1=0` represents a pair of straight lines.The distance between them is

Options

A. 4
B. `(4)/(3)`
C. 2
D. `2sqrt(3)`

Answer

C

Explanation

We have , `x^2+2sqrt(2)xy+2y^2+4x+4sqrt(2)y+1=0`
Here , `a=1,b=2,c=1 and g=2`
Now , `h^2-ab=(sqrt(2))^2-1xx2=0`
Thus , pair of lines is parallel , os distance betels them is `d=2sqrt((g^2-ac)/(a(a+b)))`
`=2sqrt((4-1)/3)`
`rArr d=2` .