$A(4,3)$ and $B(2,5)$ are two points. If $P$ is a variable point on the same side as the origin with respect to the line $AB$ and is at most at a distance of $5$ units from the midpoint of $AB$,then the locus of $P$ is
- A$x^2+y^2-6x-8y=0$
- B$x^2+y^2-6x-8y \leq 0, x+y-7 < 0$
- C$x^2+y^2+6x+8y-25=0, x+y-7 \leq 0$
- D$x^2+y^2-6x+8y \geq 0, x+y-7 < 0$
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