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Abstract: We study the family of ellipses having a fixed focal length (distance from a focus to its nearest vertex). This family includes ellipses of every possible eccentricity. When the eccentricity is near zero or one, the directrix is very far from the center of the ellipse; it comes closest to the center when the eccentricity is 1/2. We display a linkage (a contraption with sliding bars, joints and grooves) such that if one point is kept on the focus, another point follows the intersection of the directrix and the major axis. While the first point moves linearly, the second point must follow a back-and-forth motion. We conclude by discussing what happens if several such gadgets are connected in series.