Find $k$ , if the line $x + 2 = 0$ is one of the lines represented by the equation $x^{2} + 2 x y + 4 y + k = 0$ .

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Solution

Given $x + 2 = 0$ is one of the lines represented by the equation $x^{2} + 2 x y + 4 y + k = 0$ ......(1).

That means $x = - 2$ will satisfy the equation represented by (1).

Then we have,
$(- 2)^{2} + 2 \times (- 2) \times y + 4 y + k = 0$

or, $4 - 4 y + 4 y + k = 0$

or, $k = - 4$ .

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