Question

The (x,y) is equidistant from (0,0) and (4,-2). Find its algebraic equation.

Answer 1

must be on the right bisector of the line joining (0,0) and 4,-2)

slope of that line is (-2-0)/(4-0) = -1/2
so the slope of the right-bisector must be +2
and we can start by saying the equation of the right-bisector must be
y = 2x + b

but we also know that the mid point of our line segment must lie on this
midpoint = ((4+0)/2 , (-2+0)/2 ) = (2, -1)

so in y = mx + b
-1 = 3(2) + b
b = -7

y = 2x - 7