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If the curve ...

Question

If the curve $2 x^{2} + x y - y^{2} - 3 x + 4 y + k = 0$ passes through the origin, then the value of $k$ is _____

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Solution

The correct option is D $0$
If the curve $2 x^{2} + x y - y^{2} - 3 x + 4 y + k = 0$ passes through origin, this means that it passes through $(0, 0)$
Substitute $x = 0$ and $y = 0$ in $2 x^{2} + x y - y^{2} - 3 x + 4 y + k = 0$ to find the value of $k$ as follows:
$2 (0)^{2} + (0) (0) - (0)^{2} - 3 (0) + 4 (0) + k = 0$ that is $k = 0$ .

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