Question

If the slope of one line represented by $a^3{x}^2-2hxy+b^3{y}^2=0$ is square of the slope of another line, then

• A. $h=2ab(a+b)$
• B. $h=ab(a+b)$
• C. $3h=2ab(a+b)$
• D. $2h=ab(a+b)$

Answer 1

Answer: (D)

$2h=ab(a+b)$

$a^3{x}^2-2hxy+b^3{y}^2=0$
Let the slope of lines be $m_1$ and $m_2$.

Then, $m_1+m_2=\frac{2h}{b^3},m_1{m}_2=\frac{a^3}{b^3}$
Given, $m_2^2=m_1\Rightarrow m_2^3=\frac{a^3}{b^3}$
$\Rightarrow m_2=\frac{a}{b}$
Also $m_2^2+m_2=\frac{2h}{b^3}$
$\Rightarrow \frac{2h}{b^3}=\frac{a}{b}+\frac{a^2}{b^2}$

$\Rightarrow 2h=a^{2}b+a{b}^2=ab(a+b)$