Question 966935: find the equation of the set of all points.P(x,y) that is equidistant from y-axis and (4,0)
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! Perpendicular distance from (x,y) to y-axis is,
Distance from (x,y) to (4,0) is,
Set them equal to each other.
The solution is a parabola with symmetric about the x-axis.
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Let's choose a point to verify the solution.
Let  , then 
So  and 
The distance from ( , ) to ( , , ) is
which equals the distance from the y-axis so the solution checks out.
 =( , ) and (, )
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