First slide

Pair of straight lines

Question

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

Moderate

A

2
B

-1
C

1
D

-2

Solution

If $m_{1}, m_{2}$ are the slopes, then $m_{1} + m_{2} =$ $- 2 c / 7, m_{1} m_{2} = - 1 / 7$
$\begin{array}{l} m_{1} + m_{2} = 4 m_{1} m_{2} \\ c = 2 \end{array}$

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