Question

Find the asymptotes of the curve $y=\frac{3x+3}{x-3}$ .

Answer 1

Given curve $y=\frac{3x+3}{x-3}$

$xy-3y=3x+3$

$xy-3x-3y-3=0$

Pair of asymptotes is $xy-3x-3y+\lambda =0$

$\lambda =3\times 3$

$\Rightarrow \lambda =9$

$\therefore$ from equation $\left(1\right)$, $xy-3x-3y+9=0$

$x(y-3)-3(y-3)=0$

$(x-3)(y-3)=0$

$\Rightarrow x=3,y=3$

$\therefore$ Asymptotes are $x=3$, $y=3$.