The point on $x$-axis equidistant from the points $P(5,0)$ and $Q(-1,0)$ is\

Question

Professor PC Thomas Classes · Answer

(a) : Let coordinates of the point on the $x$-axis be $R(x, 0)$.\ Given, $P R=Q R \Rightarrow P R^{2}=Q R^{2}$\ $\Rightarrow(x-5)^{2}+(0-0)^{2}=(x+1)^{2}+(0-0)^{2}$\ $\Rightarrow x^{2}-10 x+25=x^{2}+2 x+1 \Rightarrow 12 x=24 \Rightarrow x=2$\ $	herefore \quad$ Required point is $(2,0)$.\