Question

Find the point on x-axis which is equidistant from points A(−1, 0) and B(5, 0). [CBSE 2013C]

Answer 1

Let P(x, 0) be the point on x-axis. Then
$$\begin{gathered} AP=BP\Rightarrow A{P}^2=B{P}^2 \\ \Rightarrow {\left(x+1\right)}^2+{\left(0-0\right)}^2={\left(x-5\right)}^2+{\left(0-0\right)}^2 \\ \Rightarrow x^2+2x+1=x^2-10x+25 \\ \Rightarrow 12x=24\Rightarrow x=2 \end{gathered}$$
Hence, x = 2.