Question

The equations of the asymptotes of the hyperbola

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

• A. $2x^{2} + 5xy + 2y^{2} - 11x - 7y - 5 = 0$
• B. $2x^{2} + 4xy + 2y^{2} - 7x - 11y + 5 = 0$
• C. $2x^{2} + 5xy + 2y^{2} - 11x - 7y + 5 = 0$
• D. None of these

Answer 1

Answer: (A)

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

Answer 2

The pair of asymptotes curve differ by a constant.

$\therefore$Pair of asymptotes

$2x^{2} + 5xy + 2y^{2} - 11x - 7y + \lambda = 0$……..……(1)

Hence (1) represents a pair of straight lines.

$\therefore\Delta = 0$

then 2 x 2 x λ + 2 x -$\frac{7}{2}$ x - $\frac{11}{2}$x $\frac{5}{2}$ - 2 x $\left( - \frac{7}{2} \right)^{2}$ - 2 x $\left( - \frac{11}{2} \right)^{2}$ - λ$\left( \frac{5}{2} \right)^{2} = 0$

$\therefore\lambda = 5$ From (1)

$\therefore$ pair of asymptotes is

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