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$A (0, 0), B (1, 2)$ are two points. If a point $P$ moves such that the area of $△ P A B$ is 2 sq. units, then the locus of $P$ is

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$4 x^{2} + 4 x y - y^{2} = 16$

$4 x^{2} - 4 x y + y^{2} = 16$

$x^{2} + 4 x y + y^{2} = 16$

$x^{2} - 4 x y - 4 y^{2} = 16$

answer is B.

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Detailed Solution

$A (0, 0), B (1, 2), P (x, y)$

$\begin{matrix} △ P A B = 2 \\ \frac{1}{2} | \begin{matrix} x - 0 & y - 0 \\ x - 1 & y - 2 \end{matrix} | = 2 \\ | x y - 2 x - x y + y | = 4 \\ 2 x - y = \pm 4 \end{matrix}$

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