Straight Line Question 5
Question: Angle between the lines $ \frac{x}{a}+\frac{y}{b}=1 $ and $ \frac{x}{a}-\frac{y}{b}=1 $ is [MP PET 1995]
Options:
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 The lines are $ bx+ay-ab=0 $ and $ bx-ay-ab=0 $ . Hence the required angle is $ {{\tan }^{-1}}| \frac{ab-(-ab)}{b^{2}+a^{2}} |={{\tan }^{-1}}| \frac{2ab}{b^{2}-a^{2}} |=2{{\tan }^{-1}}\frac{b}{a} $ .
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Answer:
Solution:
BETA
