Question

What are represented by the equation $(x-y{)}^2+(x-a{)}^2=0.$

Answer 1

Given equation: $(x-y{)}^2+(x-a{)}^2=0$

Since sum of squares is always either greater than or equal to zero thus each term individually have to be equal to zero.

$\therefore x-y=0$ $and$ $x-a=0$

$\Rightarrow x=y$ $and$ $x=a$

$\Rightarrow x=a=y$

This represents a point on the x-y plane.