Suppose: circle f 1: (x+ 1)? +y？ = 1, center f 1 (- 1, 0), radius r 1= 1.

Circle F2: (x- 1)? +y？ =9, center F2 (1, 0), radius r2=3.

The center of a moving circle is p and the radius is r.

* enclose ∴PF 1= 1+r

Endotangent ∴PF2=3-r

Pf1+pf2 =1+r+3-r = 4 = 2a (fixed value)

According to the first definition of ellipse, the locus of the center of a moving circle is ellipse a=2, C =1; b？ =3

Ellipse p: x? /4+y？ /3= 1