$A(2,3)$ and $B(-1,1)$ are two points. If $P(x,y)$ is a variable point such that $\angle APB = 90^{\circ}$,then the locus of $P$ is:
- A$x^2+y^2-x-4y+1=0$
- B$x^2+y^2+x+4y-1=0$
- C$x^2+y^2-x+4y-1=0$
- D$x^2+y^2+x-4y+1=0$
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