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

Question

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

Accepted Answer

Let the lines be $y = {m_1}x$ and $y = {m_2}x$ then

$${m_1} + {m_2} =  - {{2c} \over 7}$$ and $${m_1}{m_2} =  - {1 \over 7}$$

Given ${m_1} + {m_2} = 4m{}_1{m_2}$

$$ \Rightarrow {{2c} \over 7} =  - {4 \over 7} \Rightarrow c = 2$$

Solutions · 1