Question

lf the slope of one of the lines represented by $a^3{x}^2-2hxy+L^3{y}^2=0$ be the square of the other, then $a{L}^2,h,a^{2}L$ are in

• A. A.P
• B. G.P
• C. H.P
• D. none

Answer 1

The correct option is A A.P

$m_1+m_2=\frac{2h}{L^3}$ and $m_1{m}_2=\frac{a^3}{L^3}$

Given $m_2=m^2$

$m+m^2=\frac{2h}{L^3}$ and $m^3=\frac{a^3}{L^3}$

$\Rightarrow m=\frac{a}{L}$

$\frac{a}{L}+\frac{a^2}{L^2}=\frac{2h}{L^3}$

$\Rightarrow \frac{a{L}^2+a^{2}L}{L^3}=\frac{2h}{L^3}$

$\Rightarrow 2h=a{L}^2+a^{2}L$

$\therefore a{L}^2,h,a^{2}L$ are in AP.