Every one of those vertical green lines from the curve down to the
x-axis must be equal to the slanted line that it's connected to that
goes to the point (0,2). Not only those but also an infinite number of 
possible pairs of green lines that COULD be drawn.

Let's pick one of those pairs of green line at random, and label it
with the variable coordinates (x,y).  the bottom of the green line
must have the same x-coordinate, so it has the coodinates (x,0).





We use the distance formula

d = √(x2-x1)²+(y2-y1)²

to set the distance from (x,y) to (x,0) equal to the distance between
(x,y) to (0,2)

 
    √(x-x)²+(0-y)² = √(0-x)²+(2-y)² 

Squaring both sides takes away the radicals

     (x-x)²+(0-y)² = (0-x)²+(2-y)²

        (0)²+(-y)² = (-x)²+(2-y)²

              0+y² = x²+(4-4y+y²)

                y² = x²+4-4y+y²

                 0 = x²+4-4y

                4y = x²+4

                 y = x²+1

That's the equation.

Edwin