Pair Of Straight Lines Question 70
Question: The angle between the pair of straight lines $ x^{2}-y^{2}-2y-1=0 $ , is
[MNR 1991; UPSEAT 2000]
Options:
A) $ 90^{o} $
B) $ 60^{o} $
C) $ 75^{o} $
D) $ 36^{o} $
Show Answer
Answer:
Correct Answer: A
Solution:
Using condition $ a+b=0 $ . The correct option is A 90o Given, the equation of pair of straight Lines
$x^2−y^2−2y−1=0$
$x^2−(y^2+2y+1)=0$
$x^2−(y+1)2=0$
Equating with the standard equationa
$x^2+2bxy+by^2=0$
$a=1$
$h=0$
$b=−1$
$θ=tan^{−1}(\frac{2\sqrt {b^2−ab}}{a+b})$
$=tan^{−1}(\frac {2\sqrt {−(1)(−1)}}{1−1})=tan^{−1}(\frac{1}{0})$
$∴θ=90^\circ$
BETA
