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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 the value of $'C'$ is :


( A ) $\frac{1}{2} (a^2_2 + b^2_2 - a_1^2 - b_1^2)$
( B ) $a_1^2 - a_2^2 + b_1^2 - b_2^2$
( C ) $\sqrt{a_1^2 + b_1^2 - a_2^2 - b_2^2}$
( D ) $\frac{1}{2}(a_1^2 + a_2^2 + b_1^2 + b_2^2)$

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