Pair Of Straight Lines Question 65
Question: The straight lines joining the origin to the points of intersection of the line $ 2x+y=1 $ and curve $ 3x^{2}+4xy-4x+1=0 $ include an angle
[MP PET 1993]
Options:
A) p/2
B) p/3
C) p/4
D) p/6
Show Answer
Answer:
Correct Answer: A
Solution:
Making equation of curve homogeneous w.r.t. line $ 3x^{2}+4xy-4x(2x+y)+{{(2x+y)}^{2}}=0 $
$ \Rightarrow 3x^{2}+4xy-8x^{2}-4xy+4x^{2}+y^{2}+4xy=0 $
$ \Rightarrow x^{2}-4xy-y^{2}=0 $
Angle between these two lines is $ \tan \theta =\frac{2\sqrt{h^{2}-ab}}{a+b} $
$ =\frac{2\sqrt{4+1}}{0}=\infty $ i.e., lines are perpendicular.
BETA
