The equation `8x^2+8xy+2y^2+26x+13y+15=0` represents a pair of straight lines. The distance between them is

Options

A. `(7)/(sqrt(5))`
B. `(7)/(2sqrt(5))`
C. `sqrt((7)/(5))`
D. None of these

Answer

B

Explanation

We know that, the distance between the parallel lines given by `ax^(2)+2hxy+by^(2)+2gx+2fy+c`
`=0` is `2sqrt((g^(2)-ac)/(a(a+c)))`
here, `a=8,b=2,c=15,g=13`
`therefore`Required distance`=2sqrt((169-120)/(80))`
`=(2xx7)/(4sqrt(5))=(7)/(2sqrt(5))`