A calculus problem by D G

Define an ellipse with major axis $3$ and minor axis $2$ :

${\frac{x^2}{9} + \frac{y^2}{4} = 1}$

Now construct a second curve of fixed normal distance $d$ from the ellipse (defining positive $d$ as pointing away from the origin). What is the average value of the circumference of this curve as $d$ ranges from $0$ to $2 \pi$ ? If your answer can be expressed in the form

${A \pi^B + C E \left (-\frac{D}{F} \right )}$

for positive integers $A$ , $B$ , $C$ , $D$ , $F$ , $D$ and $F$ coprime, where $E(x)$ refers to the complete elliptic integral of the second kind, find $A + B + C + D + F$ .