If $A=(-1, 2)$ and $B=(1, -2)$ are two points and $P$ is a variable point such that the area of $\triangle PAB$ is always $1$,then the equation of the locus of $P$ is
- A$4x^2 + 4xy + y^2 = 1$
- B$x^2 + 10xy + 25y^2 - 34x - 170y = 0$
- C$x^2 - 6xy + 9y^2 + 22x - 66y - 23 = 0$
- D$16x^2 - 24xy + 9y^2 - 62x + 34y + 46 = 0$
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