Question

The asymptotes of the hyperbola $2xy-4x+y=0$ are :

• A. $(2x+1)=0$ and $(y-2)=0$
• B. $(x-1)=0$ and $(y+1)=0$
• C. $(x-y)=0$ and $(x+y)=0$
• D. none of these

Answer 1

The correct option is A $(2x+1)=0$ and $(y-2)=0$

Joint equation of asymptotes will be $2xy-4x+y+\lambda =0$........(i)

For (i) to be pair of straight lines $\lambda =-2$ using $abc+2fgh-a{f}^2-b{g}^2-c{h}^2=0$ or

$\Rightarrow \left|\begin{array}{ccc}0& 1& \frac{1}{2}\\ 1& 0& -2\\ -\frac{1}{2}& -2& \lambda \end{array}\right|=0$

$⟹2x(y-2)+(y-2)=0$

$⟹(2x+1)(y-2)=0$

$⟹2x+1=0ory=2$