If the equation of the locus of a point equidistant 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 find the value of `c`.

Options

A. `a_(1)^(2) - a_(2)^(2) + b_(1)^(2) - b_(2)^(2)`
B. `sqrt(a_(1)^(2) + b_(1)^(2) - a_(2)^(2) - b_(2)^(2))`
C. `(1)/(2) (a_(1)^(2) + a_(2)^(2) + b_(1)^(2) + b_(2)^(2))`
D. `(1)/(2) (a_(2)^(2) + b_(2)^(2) - a_(1)^(2) - b_(1)^(2))`

Answer

D