Question

Distance between the pair of lines represented by the equation $ {{x}^{2}}-6xy+9{{y}^{2}}+ $ $ 3x-9y-4=0 $ is:

• A. $ \frac{15}{\sqrt{10}} $
• B. $ \frac{1}{2} $
• C. $ \sqrt{\frac{5}{2}} $
• D. $ \frac{1}{\sqrt{10}} $
• E. $ \frac{1}{5} $

Answer 1

Answer: (C)

$ {{x}^{2}}-6xy+9{{y}^{2}}+3x-9y-4=0 $ ..(i) $ \Rightarrow $ $ (x-3y+4)(x-3y-1)=0 $ $ \therefore $ Eq. (i) represented by $ x-3y+4=0 $ ...(ii) and $ x-3y-1=0 $ ...(iii) Since, the above line is parallel. $ \therefore $ Required distance $ =\left| \frac{-4-1}{\sqrt{1+9}} \right|=\frac{5}{\sqrt{10}} $ $ =\sqrt{\frac{5}{2}} $