∴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