First slide

Pair of straight lines

Question

If $k_{1}, k_{2}$ are the sum and product of the slopes of the pair of lines $2 x^{2} + 4 xy + y^{2} = 0$ then $k_{1} + k_{2}$ is

Easy

A

$- \frac{1}{2}$
B

$\frac{1}{2}$
C

-2
D

2

Solution

If $m_{1}, m_{2}$ are slopes of lines represented by the combined equation ${ax}^{2} + 2 hxy + {by}^{2} = 0$ then $m_{1} + m_{2} = - \frac{2 h}{b}$ and $m_{1} \cdot m_{2} = \frac{a}{b}$
Given $k_{1}, k_{2}$ are the sum and product of the slopes of the pair of lines $2 x^{2} + 4 xy + y^{2} = 0$
Hence, $k_{1} = - 4$ and $k_{2} = 2$
Therefore, $k_{1} + k_{2} = - 2$

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