The lines tangent to the curve $x^{3} + 2 y^{3} + 3 x^{2} y - 2 y x^{2} + 3 x - 2 y = 0 and x^{7} - y^{4} + 2 x + 3 y = 0$ at the origin intersect at an angle $θ$ , then the value of $θ$ is equal to

\frac{π}{6}

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\frac{π}{4}

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\frac{π}{3}

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\frac{π}{2}

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Solution

The correct option is D $\frac{π}{2}$
Equation of tangent to $x^{3} + 2 y^{3} + 3 x^{2} y - 2 y x^{2} + 3 x - 2 y = 0$ at origin is $3 x - 2 y = 0$ and for $x^{7} - y^{4} + 2 x + 3 y = 0 is 2 x + 3 y = 0$
The product of their slopes is $- 1$ .
Hence, these lines are perpendicular and angle between them is $\frac{π}{2} .$

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