First slide

Pair of straight lines

Question

If the lines represented by the equations ${kx}^{2} + 2 xy + y^{2} + 2 x + 2 y + 4 = 0$ are parallel to each other then $k =$

Moderate

A

$5$
B

1
C

-1
D

-2

Solution

The condition that the equation ${ax}^{2} + 2 hxy + {by}^{2} + 2 gx + 2 fy + c = 0$ represents pair of parallel lines $h^{2} = ab, and {af}^{2} = {bg}^{2}$ is
For the equation ${kx}^{2} + 2 xy + y^{2} + 2 x + 2 y + 4 = 0$ , the values are $a = k, h = 1, b = 1$
Therefore $k = 1$ ,

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