The distance btween the parallel lines `9x^2-6xy+y^2+18x-6y+8=0`, is

Options

A. `(1)/(sqrt(10))`
B. `(1)/(sqrt(10))`
C. `(4)/(sqrt(10))`
D. `sqrt(10)`

Answer

B

Explanation

We have , `9x^2-6xy+y^2+18x-6y+8=0`
Here , `a=9,b=1,c=8and g=9`
`therefore` The distance between parallel lines , `d=2sqrt((g^2-ac)/(a(a+b)))`
`=2sqrt((81-9xx8)/(9xx10))=2sqrt((81-72)/(9xx10))`
`=2sqrt((9)/(9xx10))=2xxsqrt((1)/(10))=(2)/(sqrt(10))`.