Question

If the slope of one of the lines represented by $a{x}^2+2hxy+b{y}^2=0$ is the square of the other, then $\frac{a+b}{h}+\frac{8h^2}{ab}$ is equal to

• A. 4
• B. 6
• C. 8
• D. 9

Answer 1

The correct option is B

6

Let $mand{m}^2$ be the slopes of lines represented by $a{x}^2+2hxy+b{y}^2=0$
$\Rightarrow m+m^2=-\frac{2h}{b},m^3=\frac{a}{b}$
So, $(m+m^2{)}^3=-\frac{8h^3}{b^3}$
$\Rightarrow m^3+m^6+3m^3(m+m^2)=-\frac{8h^3}{b^3}$
$\Rightarrow \frac{a}{b}+\frac{a^2}{b^2}+\frac{8h^3}{b^3}=\frac{6ah}{b^2}$
$\frac{ab+a^2}{b^2}+\frac{8h^3}{b^3}=\frac{6ah}{b^2}a(b+a)+\frac{8h^3}{b}=6ah\frac{a+b}{h}+\frac{8h^2}{ab}=6$