Question

If $xy-4x+3y-\lambda =0$ represents the asymptotes of $xy-4x+3y=0$, then $\lambda$ is.

• A. $3$
• B. $-6$
• C. $8$
• D. $12$

Answer 1

The correct option is D $12$

$xy-4x+3y=0$

$x(y-4)+3y-12+12=0$

$x(y-4)+3(y-4)+12=0$

$(y-4)(x+3)=-12$

$(y-4)(x+3)=0$ is the joint eqn. of asymptotes

$xy-4x+3y-12=0$ represents asymptotes of

$xy-4x+3y=0$

Comparing $xy-4x+3y-12=0$ with

$xy-4x+3y-\lambda =0$

$\lambda =12$