Discussion Forum

 Which of the following options is not the asymptote of the curve

3x³+2x²y-7xy² +2y³-14xy+7y² +4x+5y=0?

Answer:

Explanation:

$\phi_{3}(m)=3+2m-7m^{2}+2m^{3}$

$\phi_{2}(m)=-14m+7m^{2}$

$\phi_{3}'(m)=2-14m+6m^{2}$

 Now, putting $\phi_{3}(m)=0$ , we have

 3+2m-7m²+2m³ =0

$\Rightarrow$      $(1-m)(1+2m)(3-m)=0$

$\Rightarrow$      $m=-\frac{1}{2},1,3$

 We know that , $c\phi_{n}'(m)+\phi_{n-1}(m)=0$ , which in the given case becomes

 c(2-14m+6m²)+(-14m+7m²)=0

$\Rightarrow c=\frac{14m-7m^{2}}{2-14m+6m^{2}}$

So, when  $m=-\frac{1}{2},c=-\frac{5}{6}$

 when m=1, c= $-\frac{7}{6}$

when m=3, c= $-\frac{3}{2}$

 Asymptotes are y= $-\frac{1}{2}$ x $-\frac{5}{6}$,

 $y=x-\frac{7}{6}$and   $y=3x-\frac{3}{2}$