Question

The asymptotes of the hyperbola $x y-3 x-2 y=0$ 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

Answer: (A)

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