Question

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

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is C

Equation of hyperbola is
$2x^2+5xy+2y^2-11x-7y-4=0$ …… (i)
Let asymptotes of the hyperbola (i) be
$2x^2+5xy+2y^2-11x-7y+c=0$ …… (ii)
Since, equation (ii) represents a pair of lines.
$\therefore$ $\left|\begin{array}{ccc}2& 5/2& -11/2\\ 5/2& 2& -7/2\\ -11/2& -7/2& c\end{array}\right|=0$
$\Rightarrow -\frac{11}{2}(-\frac{35}{4}+11)+\frac{7}{2}(-7+\frac{55}{4})+c(4-\frac{25}{4})=0$ $\Rightarrow$ $\frac{9}{4}c=-\frac{99}{8}+\frac{189}{8}=\frac{90}{8}\Rightarrow c=5$ $\therefore$
Equation of the required asymptotes is
$2x^2+5xy+2y^2-11x-7y+5=0$