If the equation of the locus of a point equidistant from the point $\left( {{a_{1,}}{b_1}} \right)$ and $\left( {{a_{2,}}{b_2}} \right)$ is $\left( {{a_1} - {a_2}} \right)x + \left( {{b_1} - {b_2}} \right)y + c = 0$ , then the value of $'c'$ is :

Question

If the equation of the locus of a point equidistant from the point $\left( {{a_{1,}}{b_1}} \right)$ and $\left( {{a_{2,}}{b_2}} \right)$ is
$\left( {{a_1} - {a_2}} \right)x + \left( {{b_1} - {b_2}} \right)y + c = 0$ , then the value of $'c'$ is :

$\sqrt {{a_1}^2 + {b_1}^2 - {a_2}^2 - {b_2}^2} $

${1 \over 2}\left( {{a_2}^2 + {b_2}^2 - {a_1}^2 - {b_1}^2} \right)$

${{a_1}^2 - {a_2}^2 + {b_1}^2 - {b_2}^2}$

${1 \over 2}\left( {{a_1}^2 + {a_2}^2 + {b_1}^2 + {b_2}^2} \right)$.

Solution

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