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Mathematical trajectory
Point p is a point on the perpendicular of line segment AB,

∴PA=PB.

PB+PF=BF=R=2。

∴PA+PF=2

That is, the sum of the distances from the moving point P to the two fixed points A (-1/2,0) and F (1/2,0).

Is the constant 2.

According to "the first definition of ellipse"

The trajectory of the fixed point P is concentrated in two fixed points A (-1/2,0) and F (1/2,0).

Ellipse with major axis =2.

Let its equation be (x? /a? )+(y? /b? )= 1 (a>b>0)

As can be seen from the above, a = 1, c = 1/2, and b = √ (a? -c? )=(√3)/2

∴a? = 1,b? =3/4

∴' s trajectory equation is

(x? )+(4y? /3)= 1