Question

If the slopes of the lines given by $8x^3+a{x}^{2}y+bx{y}^2+y^3=0$ are in G. P., then

• A. $a=b$
• B. $2a=b$
• C. $a=2b$
• D. $a+b=0$

Answer 1

The correct option is C $a=2b$

$m+\frac{m}{r}+mr=-b$
$\Rightarrow \frac{m^2}{r}+m^2+m^{2}r=a$
$\Rightarrow m^3=-8$
$\Rightarrow m=-2$

Now,
$1+\frac{1}{r}+r=\frac{-b}{m}$
$\Rightarrow 1+\frac{1}{r}+r=\frac{a}{m^2}$
$\Rightarrow \frac{-b}{m}=\frac{a}{m^2}$
$\Rightarrow a=-mb$
$\Rightarrow a=2b$