A) \[\frac{15}{\sqrt{10}}\]
B) \[\frac{1}{2}\]
C) \[\sqrt{\frac{5}{2}}\]
D) \[\frac{1}{\sqrt{10}}\]
E) \[\frac{1}{5}\]
Correct Answer: C
Solution :
\[{{x}^{2}}-6xy+9{{y}^{2}}+3x-9y-4=0\] ..(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 \[=\left| \frac{-4-1}{\sqrt{1+9}} \right|=\frac{5}{\sqrt{10}}\] \[=\sqrt{\frac{5}{2}}\]
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