Pair Of Straight Lines Question 139
Question: If the angle between the lines represented by the equation $ y^{2}+kxy-x^{2} $
$ {{\tan }^{2}}A=0 $ be $ 2A $ , then $ k= $
Options:
A) 0
B) 1
C) 2
D) $ \tan A $
Show Answer
Answer:
Correct Answer: A
Solution:
Here $ \tan 2A=\frac{2\sqrt{\frac{k^{2}}{4}+{{\tan }^{2}}A}}{1-{{\tan }^{2}}A} $
$ \Rightarrow \frac{2\tan A}{1-{{\tan }^{2}}A}=\frac{2\sqrt{\frac{k^{2}}{4}+{{\tan }^{2}}A}}{1-{{\tan }^{2}}A} $
$ \Rightarrow \frac{k^{2}}{4}+{{\tan }^{2}}A={{\tan }^{2}}A\Rightarrow k=0 $ .
BETA
