The straight lines joining the origin to the points of intersection of the line 2x + y = 1 and curve $3 x^{2} + 4 x y - 4 x + 1 = 0$ include an angle

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Solution

The correct option is A

Making equation of curve homogeneous w.r.t line $3 x^{2} + 4 x y - 4 x (2 x + y) + (2 x + y)^{2} = 0$

$\Rightarrow 3 x^{2} + 4 x y - 8 x^{2} - 4 x y + 4 x^{2} + y^{2} + 4 x y = 0$

$\Rightarrow x^{2} - 4 x y - y^{2} = 0$

Angle between these two lines is $tan θ = \frac{2 \sqrt{h^{2} - a b}}{a + b} = \frac{2 \sqrt{4 + 1}}{0} = \infty$ i.e., lines are perpendicular.

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