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If the equation of the locus of a point equidistant from the points \( \left(a_{1}, b_{1}\right) \) and \( \left(a_{2}, b_{2}\right) \) is \( \left(a_{1}-a_{2}\right) x+\left(b_{1}-b_{2}\right) y+c=0 \),
P then the value of \( c \) is

W
(1) \( a_{1}^{2}-a_{2}^{2}+b_{1}^{2}-b_{2}^{2} \)
(2) \( \sqrt{a_{1}^{2}+b_{1}^{2}-a_{2}^{2}-b_{2}^{2}} \)
(3) \( \frac{1}{2}\left(a_{1}^{2}+a_{2}^{2}+b_{1}^{2}+b_{2}^{2}\right) \)
(4) \( \frac{1}{2}\left(a_{2}^{2}+b_{2}^{2}-a_{1}^{2}-b_{1}^{2}\right) \)
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