The equation of the asymptotes of the hyperbo | vedclass

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(B) The equation of the asymptotes of the hyperbola $2 x^2+5 x y+2 y^2-11 x-7 y-4=0$ is of the form $2 x^2+5 x y+2 y^2-11 x-7 y+\lambda=0$. Since this

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$2 x^2+5 x y+2 y^2-11 x-7 y+5=0$

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(B) The equation of the asymptotes of the hyperbola $2 x^2+5 x y+2 y^2-11 x-7 y-4=0$ is of the form $2 x^2+5 x y+2 y^2-11 x-7 y+\lambda=0$. Since this represents a pair of straight lines,the determinant of the general second-degree equation must be zero: $abc + 2fgh - af^2 - bg^2 - ch^2 = 0$. Here,$a=2, b=2, c=\lambda, h=\frac{5}{2}, g=-\frac{11}{2}, f=-\frac{7}{2}$. Substituting these values: $2(2)(\lambda) + 2(-\frac{7}{2})(-\frac{11}{2})(\frac{5}{2}) - 2(-\frac{7}{2})^2 - 2(-\frac{11}{2})^2 - \lambda(\frac{5}{2})^2 = 0$. $4\lambda + \frac{385}{4} - \frac{49}{2} - \frac{121}{2} - \frac{25\lambda}{4} = 0$. Multiplying by $4$: $16\lambda + 385 - 98 - 242 - 25\lambda = 0$. $-9\lambda + 45 = 0 \Rightarrow \lambda = 5$. Thus,the equation is $2 x^2+5 x y+2 y^2-11 x-7 y+5=0$.

The equation of the asymptotes of the hyperbola $2 x^2+5 x y+2 y^2-11 x-7 y-4=0$ is

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