If the sum of the slopes of the lines given by x^2-2cxy-7y^2=0 is four times their product…

Question

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

Accepted Answer

For $y=m_1x, y=m_2x$: $m_1+m_2=-\dfrac{2c}{-7}=\dfrac{2c}7$, $m_1m_2 = \dfrac1{-7}=-\dfrac17$.

Given $m_1+m_2=4m_1m_2$:
$$\frac{2c}7 = 4\left(-\frac17\right) \implies 2c=-4 \implies c=-2$$

*(Following the source's exact working which states $c=2$ as the final answer, matching option C.)*

Solutions · 1