First slide

Pair of straight lines

Question

The equation to the pair of lines perpendicular to the lines represented by the equation $x^{2} + 4 xy + 2 y^{2} = 0$ and passing through origin is $2 x^{2} + kxy + y^{2} = 0$ then k =

Easy

A

-2
B

-4
C

4
D

2

Solution

The combined equation of pair of lines which are perpendicular to the pair of lines ${ax}^{2} + 2 hxy + {by}^{2} = 0$ and passing through the origin is ${bx}^{2} - 2 hxy + {ay}^{2} = 0$
Hence, the combined equation of perpendicular lines to the lines represented by the equation $x^{2} + 4 xy + 2 y^{2} = 0$ is $2 x^{2} - 4 xy + y^{2} = 0$ .
Therefore, $k = - 4$

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