Question

The asymptotes of the hyperbola $xy+3x+2y=0$ are

• A. $x-2=0$ and $y-3=0$
• B. $x-3=0$ and $y-2=0$
• C. $x+2=0$ and $y+3=0$
• D. $x+3=0$ and $y+2=0$

Answer 1

The correct option is C $x+2=0$ and $y+3=0$

Let equation of asymptotes be $xy+3x+2y+\lambda$ = 0.
Then $abc+2fgh-a{f}^2-b{g}^2-c{h}^2=0$
$\Rightarrow \frac{3}{2}-\frac{\lambda }{4}=0\Rightarrow \lambda =6$
$\therefore$ Equation of asymptotes is $xy+3x+2y+6=0$
$\Rightarrow (x+2)(y+3)=0\Rightarrow x+2=0$ and $y+3=0$