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

Show Answer

Answer:

Correct Answer: A

Solution:

  • 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} $ .