A) \[{{90}^{o}}\]
B) \[{{60}^{o}}\]
C) \[{{75}^{o}}\]
D) \[{{36}^{o}}\]
Correct Answer: A
Solution :
Key Idea: If the equation of pair of lines is \[a{{x}^{2}}+2hxy+b{{y}^{2}}+2gx+2fy+c=0\], then \[\theta =\frac{2\sqrt{{{h}^{2}}-ab}}{a+b}\] Given equation of pair of lines is \[{{x}^{2}}-{{y}^{2}}-2xy-1=0\] Here, \[a=1,\,\,b=-1,\,\,h=-1\] \[\therefore \] \[\tan \theta =\frac{2\sqrt{{{(-1)}^{2}}+1}}{1-1}=\infty \] Note: If \[{{h}^{2}}=ab\], then the pair of lines are parallel.
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