Posted by Princess Mae Campana on .
The (x,y) is equidistant from (0,0) and (4,2). Find its algebraic equation.

analytic geometry 
Reiny,
must be on the right bisector of the line joining (0,0) and 4,2)
slope of that line is (20)/(40) = 1/2
so the slope of the rightbisector must be +2
and we can start by saying the equation of the rightbisector 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