Pair Of Straight Lines Question 114
Question: The area (in square units) of the quadrilateral formed by the two pairs of lines $ l^{2}x^{2}-m^{2}y^{2}-n(lx+my)=0 $ and $ l^{2}x^{2}-m^{2}y^{2}+n(lx-my)=0 $ is
[EAMCET 2003]
Options:
A) $ \frac{n^{2}}{2|lm|} $
B) $ \frac{n^{2}}{|lm|} $
C) $ \frac{n}{2|lm|} $
D) $ \frac{n^{2}}{4|lm|} $
Show Answer
Answer:
Correct Answer: A
Solution:
Given lines are (on factorising) $ lx+my=0,lx+my+n=0 $
$ lx-my=0,lx+my-n=0 $ Area = $ | \frac{(c_1-d_1)(c_2-d_2)}{(a_1b_2-a_2b_1)} |=| \frac{(0-n)(0+n)}{(-lm-lm)} |=\frac{n^{2}}{2|lm|} $ .
BETA
