Pair Of Straight Lines Question 91
Question: The acute angle formed between the lines joining the origin to the points of intersection of the curves $ x^{2}+y^{2}-2x-1=0 $ and $ x+y=1 $ , is
[MP PET 1998]
Options:
A) $ {{\tan }^{-1}}( -\frac{1}{2} ) $
B) $ {{\tan }^{-1}}2 $
C) $ {{\tan }^{-1}}\frac{1}{2} $
D) $ 60^{o} $
Show Answer
Answer:
Correct Answer: B
Solution:
From $ x+y=1, $ to make the curve $ x^{2}+y^{2}-2x-1=0 $ homogenous.
$ \Rightarrow x^{2}+y^{2}-2x(x+y)-{{(x+y)}^{2}}=0 $
$ \therefore 2x^{2}+4xy=0 $ or $ x^{2}+2xy=0 $
$ \therefore \tan \theta =\frac{2\sqrt{h^{2}-ab}}{a+b} $ and $ a=1,\ b=0,\ h=1 $
$ \therefore \tan \theta =\frac{2\sqrt{1^{2}-0}}{1}\Rightarrow \theta ={{\tan }^{-1}}(2) $ .
BETA
