Question

If the slope of one of the lines represented by $a{x}^2+2hxy+b{y}^2=0$ is square of the other then $ab(a+b)+8h^3$

• A. $4abh$
• B. $5abh$
• C. $6abh$
• D. $8abh$

Answer 1

Answer: (C)

$6abh$

$a{x}^2+2hxy+b{y}^2$

Let are slope is $m$ and other is $m^2$

$-(m+m^2)=\frac{2h}{b}{m}^3=\frac{a}{b}$

$-m(m+1)=\frac{2h}{b}m=\sqrt[3]{3\frac{a}{b}}$

$\sqrt[3]{3\frac{a}{b}}(\sqrt[3]{3\frac{a}{b}}+1)=\frac{2h}{b}$

on solving we get $a^{2}b+a{b}^2+8h^3=6abh$

$C$ is correct.