The equation of a hyperbola , conjugate to the hyperbola $x^{2} + 3 x y + 2 y^{2} + 2 x + 3 y = 0 i s$

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Solution

The correct option is B

Let $H = x^{2} + 3 x y + 2 y^{2} + 2 x + 3 y = 0 a n d C = 0$ is its conjugate. Then C + H=2A, where A=0 is the combined equation of asymptotes. Equation of asymptotes is , $x^{2} + 3 x y + 2 y^{2} + 2 x + 3 y + λ = 0$ where $Δ = a b c + 2 f g h - a f^{2} - b g^{2} - c h^{2} = 0 \Rightarrow λ = 1$ $∴ C = 2 (x^{2} + 3 x y + 2 y^{2} + 2 x + 3 y + 1) - (x^{2} + 2 y^{2} + 3 x y + 2 x + 3 y)$ $\Rightarrow$ equation of conjugate hyperbola is $x^{2} + 3 x y + 2 y^{2} + 2 x + 3 y + 2 = 0$

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