Question

The equation 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

The correct option is C $2x^2+5xy+2y^2-11x-7y+5=0$

Pair of asymptotes of the curve differe by the constant only
$\therefore$ Pair of asymptotes of $2x^2+5xy+2y^2-11x-7y-4=0$ are given by
$2x^2+5xy+2y^2-11x-7y+\lambda =0$, which represent a pair of straight lines if
$△=abc+2fgh-a{f}^2-b{g}^2-c{h}^2=0$ where
$a=2=b,h=\frac{5}{2},g=\frac{-11}{2},f=-\frac{7}{2},c=\lambda$
$\therefore △=2\times 2\times \lambda +2(-\frac{7}{2})(-\frac{11}{2})\left(\frac{5}{2}\right)-2{(-\frac{7}{2})}^2-2{(-\frac{11}{2})}^2-\lambda {\left(\frac{5}{2}\right)}^2=0$
$\Rightarrow \lambda =5$
$\therefore$ Pair of asymptotes is given by
$2x^2+5xy+2y^2-11x-7y+5=0$
Hence choice (c) is correct answer.