A) \[\frac{6}{5}\]
B) \[\frac{6}{\sqrt{10}}\]
C) \[\frac{6}{\sqrt{5}}\]
D) \[\frac{3}{2}\]
Correct Answer: B
Solution :
Given equation of pair of parallel lines is \[{{x}^{2}}+6xy+9{{y}^{2}}+4x+12y-5=0\] ...(i) On comparing this equation with general equation of second degree \[a{{x}^{2}}+2hxy+b{{y}^{2}}+2gx+2fy+c=0\] we get \[a=1,\text{ }h=3,\text{ }b=9,\text{ }g=2,\text{ }f=6,\text{ }c=-5\] Now, distance between the parallel lines represented by Eq. (i) is given by \[2\sqrt{\frac{{{g}^{2}}-ac}{a(a+b)}}=2\sqrt{\frac{4+5}{1(10)}}\] \[=2.\frac{3}{\sqrt{10}}=\frac{6}{\sqrt{10}}\]
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