Question

If P(x, y) is equidistant from the points A(7, 1) and B(3, 5), find the relation between x and y.

Answer 1

Let the point $P\left(x,y\right)$ be equidistant from the points A(7, 1) and B(3, 5).
Then,
$$\begin{gathered} PA=PB \\ \Rightarrow P{A}^2=P{B}^2 \\ \Rightarrow {\left(x-7\right)}^2+{\left(y-1\right)}^2={\left(x-3\right)}^2+{\left(y-5\right)}^2 \\ \Rightarrow x^2+y^2-14x-2y+50=x^2+y^2-6x-10y+34 \\ \Rightarrow 8x-8y=16 \\ \Rightarrow x-y=2 \end{gathered}$$