The point P$(x$, 1) is the same distance from A(-2, 5) as it is from B(4, 3).
Find P.

Equate the squared distances: $(x+2{)}^2+(1-5{)}^2=(x-4{)}^2+(1-3{)}^2$, so $x^2+4x+20=x^2-8x+20$. The constants cancel, leaving $12x=0$ and $x=0$, so P is (0, 1). Check: it is $\sqrt{4+16}=\sqrt{20}$ from A and $\sqrt{16+4}=\sqrt{20}$ from B. Dropping the sign on -2 and writing $(x-2{)}^2$ instead is what produces the wrong point (1, 1).