Pair Of Straight Lines Question 82
Question: If the acute angles between the pairs of lines $ 3x^{2}-7xy+4y^{2}=0 $ and $ 6x^{2}-5xy+y^{2}=0 $ be $ {\theta_1} $ and $ {\theta_2} $ respectively, then
Options:
A) $ {\theta_1}={\theta_2} $
B) $ {\theta_1}=2{\theta_2} $
C) $ 2{\theta_1}={\theta_2} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Obviously $ {\theta_1}={{\tan }^{-1}}( \frac{2\sqrt{\frac{49}{4}-12}}{3+4} )={{\tan }^{-1}}( \frac{1}{7} ) $ and $ {\theta_2}={{\tan }^{-1}}( \frac{2\sqrt{\frac{25}{4}-6}}{6+1} )={{\tan }^{-1}}( \frac{1}{7} ) $ . Hence, $ {\theta_1}={\theta_2} $ .
BETA
