Write an equation for a parabola in which the set of all points in the plane are equidistant from the focus and line.
For the point (x, y) the distance from F is sqrt((x+2)^2 + y^2), from the line x=2 is |x-2|. They have to be equal.Raise the equation to the second degree:
(x+2)^2 + y^2 = |x-2|^2 = (x-2)^2 and open brackets:
x^2 + 4x + 4 + y^2 = x^2 - 4x + 4,4x + y^2 = -4x,
x = -y^2/8.
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