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

For the general equation of a pair of straight lines through the origin, $A{x}^2+2Hxy+B{y}^2=0$:
The sum of slopes $m_1+m_2=\frac{-2H}{B}.$
The product of slopes $m_1{m}_2=\frac{A}{B}.$
Given equation: $x^2-2cxy-7y^2=0$.
Here $A=1,2H=-2c,$ and $B=-7$.
Sum of slopes $=\frac{-(-2c)}{-7}=-\frac{2c}{7}$.
Product of slopes $=\frac{1}{-7}=-\frac{1}{7}$.
Given that the sum of slopes is four times the product:
$-\frac{2c}{7}=4(-\frac{1}{7})$
$-2c=-4\Rightarrow c=2$.