Pair Of Straight Lines Question 63
Question: . If $ (a+3b)(3a+b)=4h^{2} $ , then the angle between the lines represented by $ ax^{2}+2hxy+by^{2}=0 $ is
Options:
A) $ 30^{o} $
B) $ 45^{o} $
C) $ 60^{o} $
D) $ {{\tan }^{-1}}\frac{1}{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \theta ={{\tan }^{-1}}( \frac{2\sqrt{h^{2}-ab}}{a+b} )={{\tan }^{-1}}( \frac{\sqrt{4h^{2}-4ab}}{a+b} ) $
$ ={{\tan }^{-1}}( \frac{\sqrt{3a^{2}+3b^{2}+10ab-4ab}}{a+b} )=60{}^\circ $ .
BETA
