Find the point on x-axis which is equidistant from points A(−1, 0) and B(5, 0).


Find the point on x-axis which is equidistant from points A(−1, 0) and B(5, 0).      


Let P(x, 0) be the point on x-axis. Then

$A P=B P \Rightarrow A P^{2}=B P^{2}$


$\Rightarrow x^{2}+2 x+1=x^{2}-10 x+25$

$\Rightarrow 12 x=24 \Rightarrow x=2$

Hence, x = 2.


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