Question

If the sum of the slopes of the lines given by $x^2-2cxy-7y^2=0$ is four times their product, then the value of $c$ is

Answer 1

Answer: 2

Let the lines be $y=m_{1}x$ and $y=m_{2}x$ then
$m_1+m_2=-\frac{2c}{7}$ and $m_1{m}_2=-\frac{1}{7}$
Given $m_1+m_2=4m_1{m}_2$
$\Rightarrow -\frac{2c}{7}=-\frac{4}{7}$
$\Rightarrow c=2$