∴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