Question

If the slope of one of the lines represented by $a{x}^2+2hxy+b{y}^2=0$ be the square of the other, then

• A. $a^{2}b+a{b}^2-6abh+8h^3=0$
• B. $a^{2}b+a{b}^2+6abh+8h^3=0$
• C. $a^{2}b+a{b}^2-3abh+8h^3=0$
• D. $a^{2}b+a{b}^2-6abh-8h^3=0$

Answer 1

The correct option is A $a^{2}b+a{b}^2-6abh+8h^3=0$

This is the equation of the line so ,

$(y-mx)(y-m^{2}x)=0$

$m^3{x}^2-(m^2+m)xy+y^2=0$

$a=m^3$

$h=-\left(\frac{m^2+m}{2}\right)$

$b=1$

$\left(\frac{a+b}{h}\right)+\left(\frac{8h^2}{ab}\right)=-\left(\frac{2(m^2-m+1)}{m}\right)+\frac{2{(m+1)}^2}{m}$

$\left(\frac{a+b}{h}\right)+\left(\frac{8h^2}{ab}\right)=6$

$a^{2}b+a{b}^2-6abh+8h^3=0$

Thus answer will be option A