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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$2 x^{2} + 4 x y + 2 y^{2} - 7 x - 11 y + 5 = 0$

$2 x^{2} + 5 x y + 2 y^{2} = 0$

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

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

answer is C.

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Detailed Solution

The equation of hyperbola is $2 x^{2} + 5 x y + 2 y^{2} - 11 x - 7 y - 4 = 0 . . . . . . (1)$

Let asymptotes of the hyperbola (1) be $2 x^{2} + 5 x y + 2 y^{2} - 11 x - 7 y + c = 0 . . . . . . (2)$

Since, Eq (2) represent pair of lines

$∴ |\begin{array}{ccc} 2 & 5 / 2 & - 11 / 2 \\ 5 / 2 & 2 & - 7 / 2 \\ - 11 / 2 & - 7 / 2 & c \end{array}| = 0$

$\Rightarrow - \frac{11}{2} (- \frac{35}{4} + 11) + \frac{7}{2} (- 7 + \frac{55}{4}) + c (4 - \frac{25}{4}) = 0$

$\Rightarrow \frac{9}{4} c = - \frac{99}{8} + \frac{189}{8} = \frac{90}{8} \Rightarrow c = 5$

$∴$ equation of the required asymptotes is

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

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