Question

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

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

Answer 1

Answer: (A)

Let the equation of asymptotes be
$2x^2+5xy+2y^2+4x+5y+\lambda =\mathrm{0.......}\left(1\right)$
This equation represents a pair of straight lines,
$\therefore abc+2fgh-a{f}^2-b{g}^2-c{h}^2=0$
$\therefore 4\lambda +25-\frac{25}{2}-8-\lambda \times \frac{25}{4}=0$
$\Rightarrow -\frac{9\lambda }{4}+\frac{9}{2}=0\Rightarrow \lambda =2$
Putting the value of $\lambda$ in eq. $\left(1\right)$, we get
$2x^2+5xy+2y^2+4x+5y+2=0$
this is the equation of the asymptotes.