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If the equation of the locus of a point equi-distant from the points `(a_(1), b_(1))` and `(a_(2),b_(2))` is `(a_(1)-a_(2))x+(b_(1)-b_(2))y+c=0` then the value of c is

A

`sqrt(a_(1)^(2)+b_(1)^(2)-a_(2)^(2)-b_(2)^(2))`

B

`(1)/(2)(a_(2)^(2)+b_(2)^(2)-a_(1)^(2)-b_(1)^(2))`

C

`a_(1)^(2)-a_(2)^(2)+b_(1)^(2)-b_(2)^(2)`

D

`(1)/(2)(a_(1)^(2)+a_(2)^(2)+b_(1)^(2)+b_(2)^(2))`

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