Pair Of Straight Lines Question 132
Question: Difference of slopes of the lines represented by equation $ x^{2}({{\sec }^{2}}\theta -{{\sin }^{2}}\theta )-2xy\tan \theta +y^{2}{{\sin }^{2}}\theta =0 $ is
[Kurukshetra CEE 2002]
Options:
A) 4
B) 3
C) 2
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
We know that $ m_1-m_2=\sqrt{{{(m_1+m_2)}^{2}}-4m_1m_2} $
$ =\sqrt{{{( \frac{2\tan \theta }{{{\sin }^{2}}\theta } )}^{2}}-4( \frac{{{\sec }^{2}}\theta -{{\sin }^{2}}\theta }{{{\sin }^{2}}\theta } )} $
$ =\sqrt{\frac{4{{\tan }^{2}}\theta }{{{\sin }^{4}}\theta }-4({{\sec }^{2}}\theta cose{c^{2}}\theta -1)}=2 $ .
BETA
