Pair Of Straight Lines Question 102
Question: The equation of the bisectors of angle between the lines represented by equation $ {{(y-mx)}^{2}}={{(x+my)}^{2}} $ is
Options:
A) $ mx^{2}+(m^{2}-1)xy-my^{2}=0 $
B) $ mx^{2}-(m^{2}-1)xy-my^{2}=0 $
C) $ mx^{2}+(m^{2}-1)xy+my^{2}=0 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
The equation is $ y^{2}+m^{2}x^{2}-2mxy-x^{2}-m^{2}y^{2}-2mxy=0 $
$ \Rightarrow x^{2}(m^{2}-1)+y^{2}(1-m^{2})-4mxy=0 $
Therefore, the equation of bisectors is $ \frac{x^{2}-y^{2}}{xy} $
$ =\frac{(m^{2}-1)-(1-m^{2})}{-2m} $
$ \Rightarrow mx^{2}+(m^{2}-1)xy-my^{2}=0 $ .
BETA
