A) \[{{45}^{o}}\]
B) \[{{60}^{o}}\]
C) \[{{90}^{o}}\]
D) \[{{30}^{o}}\]
Correct Answer: A
Solution :
Comparing given equation with \[a{{x}^{2}}+2hxy+b{{y}^{2}}+2gx+2fy+c=0\] we get \[a=1,\,h=-1/2,\,b=-6,g=-\frac{7}{2},\,f=\frac{31}{2},\,c=-18\] Now angle between the lines \[\theta ={{\tan }^{-1}}\left| \,\frac{2\sqrt{{{\left( \frac{-1}{2} \right)}^{2}}-1\times (-6)}}{1+(-6)}\, \right|={{\tan }^{-1}}\left| \,\frac{2\sqrt{\frac{1}{4}+6}}{-5}\, \right|\] \[={{\tan }^{-1}}\left| \,\frac{\left( 2\times \frac{5}{2} \right)}{-5} \right|\]=\[{{\tan }^{1}}|-1|\] = \[{{\tan }^{-1}}(1)\]=\[\frac{\pi }{4}\] or \[{{45}^{o}}\].
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