A) p/2
B) p/3
C) p/4
D) p/6
Correct Answer: A
Solution :
Making equation of curve homogeneous w.r.t. line \[3{{x}^{2}}+4xy-4x(2x+y)+{{(2x+y)}^{2}}=0\] \[\Rightarrow 3{{x}^{2}}+4xy-8{{x}^{2}}-4xy+4{{x}^{2}}+{{y}^{2}}+4xy=0\] \[\Rightarrow {{x}^{2}}-4xy-{{y}^{2}}=0\] 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.
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