The second definition of (1) ellipse: the ratio of the distance from the fixed point (c, 0) on the plane to the fixed line L: x = a 2/c (f is not on L) is a constant c/a (that is, eccentricity e, 0)

⑵ Definition of elliptic directrix: The coordinate of point P on ellipse (x0, y0). When the ratio of the distance from moving point P to fixed point O and to fixed line X is always less than 1, the straight line is an elliptic directrix.

The equation in the figure indicates that the ratio of the distance from point (x, y) to point (1, 0) to the distance of straight line x=4 is 1/2, so: ① the definition of ellipse is satisfied, and the motion trajectory of moving point is ellipse; ② The straight line x=4 is the directrix of the ellipse, and a 2/c = 4; ③ The ratio is 1/2, that is, eccentricity e = c/a and c/a = 1/2.

Reference:

[1].Ellipse _ Baidu Encyclopedia/item/%E6% A4% AD% E5% 9c% 86/684466? adapt = 1 & amp； Fr = Aladdin

[2]. Alignment Equation _ Baidu Encyclopedia/Item/%E5% 87% 86% E7% Ba% BF% E6% 96% B9% E7% A8% 8B/725084? adapt = 1 & amp； Fr = Aladdin