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The locus of the centers of the circles ...

The locus of the centers of the circles such that the point (2, 3) is the mid point of the chord `5x+2y=16` is

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`5x+2y=16`
`y=-5/2x+8`
Slope of OD=m
Slope of AB=-5/2
OD`_|_`AB
`m*-5/2=-1`
`m=2/5`
`y=mx+c`
...
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