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Directrix is a line perpendicular to the major axis of the ellipse, which is at a distance a/e from the center of ellipse on either side, where e is the eccentricity of the ellipse.

Eccentricity of ellipse is the ratio of distance of a focus from the center of ellipse to the semi major axis.

Directrix is the line from which the distance of a point P on ellipse and the distance of that point P from a focus F are in a fixed ratio, namely the (1/eccentricity).
        b² = a²(1-e²)           x²/a² + y²/b² = 1

       px+qy+r =0       P = (x1, y1)

        (x1-ae)²  + y1² =  ( p x1 + q y1 + r )² / (p² + q²)

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