A) \[2{{\tan }^{-1}}\frac{b}{a}\]
B) \[{{\tan }^{-1}}\frac{2ab}{{{a}^{2}}+{{b}^{2}}}\]
C) \[{{\tan }^{-1}}\frac{{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}\]
D) None of these
Correct Answer: A
Solution :
The lines are \[bx+ay-ab=0\]and\[bx-ay-ab=0\]. Hence the required angle is \[{{\tan }^{-1}}\left| \frac{ab-(-ab)}{{{b}^{2}}+(-{{a}^{2}})} \right|={{\tan }^{-1}}\left| \frac{2ab}{{{b}^{2}}-{{a}^{2}}} \right|=2{{\tan }^{-1}}\frac{b}{a}\].
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