Let the coordinates of the center of this circle be P(x, y) and the radius of this circle be r.

The standard rounding equation is: (x+2) 2+y 2 = 36 (the center of the circle is b).

Because there is a circle inscribed, Pb = 6-R.

And because a is on the circle p, pa = R.

Pa+Pb = 6

Defined by the first definition of ellipse.

The trajectory is an ellipse with (-2,0) and (2,0) as the focus and 2a=6 as the long axis.

So the equation is: x 2/9+y 2/5 = 0.

2. let |PF 1|=m, |PF2|=n, and the angle F 1PF2 is set to v.

In triangle F 1PF2, cosine theorem

cosv=(m^2+n^2-4c^2)/(2mn)

=[(m+n)^2-4c^2-2mn]/2mn——(m+n=2a)

=(4b^2-2mn)/2mn

=(36-2mn)/2mn

0 & ltmn & lt0.5(m+n)^2=50

So mn= 18 exists to make cosv=0.

(sinv)'=cosv

0 & ltv & lt 180

So when cosv=0, sinv takes the maximum value of 1.

(PS, m, n = 5 7s at this time, which happens to be a right triangle)