Distance between the pair of lines represented by the equation `x^(2)-6xy+9y^(2)+3x-9y-4=0`, is

Options

A. `(15)/(sqrt(10))`
B. `(1)/(2)`
C. `sqrt((5)/(2))`
D. `(1)/(sqrt(10))`

Answer

C

Explanation

The distance between the pair of straight lines given by
`ax^(2)+2hxyt+by^(2)+2gx+2fy+c=0`
is `=2sqrt((g^(2)-ac)/(a(a+b)))`
Here, a=1,b=9,c=-4,g=`(3)/(2)`
Required distance
`=2sqrt((9//4)-(-4))/(1(1+9)))`
`=2sqrt((25//4)/(10))=sqrt((5)/(2))`