Pair Of Straight Lines Question 61
Question: The equation $ 2x^{2}+4xy-py^{2}+4x+qy+1=0 $ will represent two mutually perpendicular straight lines, if
Options:
A) p = 1 and q = 2 or 6
B) p = 2 and q = 0 or 6
C) p = 2 and q = 0 or 8
D) p = - 2 and q = - 2 or 8
Show Answer
Answer:
Correct Answer: C
Solution:
Here equation is $ 2x^{2}+4xy-py^{2}+4x+qy+1=0 $ . The lines are perpendicular, if $ a+b=0 $
$ \Rightarrow 2-p=0\Rightarrow p=2 $ and it will represent two lines, if $ abc+2fgh-af^{2}-bg^{2}-ch^{2}=0 $
$ \Rightarrow 2(-2)(1)+2( \frac{q}{2} )(2)(2)-2{{( \frac{q}{2} )}^{2}}+2{{(2)}^{2}}-1{{(2)}^{2}}=0 $
$ \Rightarrow q^{2}-8q=0\Rightarrow q=0 $ or 8.
BETA
