# Problem 525: Rolling Ellipse
An ellipse E(a, b) is given at its initial position by equation:
\$\\frac {x\^2} {a\^2} + \\frac {(y - b)\^2} {b\^2} = 1\$ The ellipse
rolls without slipping along the x axis for one complete turn.
Interestingly, the length of the curve generated by a focus is
independent from the size of the minor axis: \$F(a,b) = 2 \\pi \\text{ }
max(a,b)\$ This is not true for the curve generated by the ellipse
center. Let C(a,b) be the length of the curve generated by the center of
the ellipse as it rolls without slipping for one turn. You are given
C(2, 4) \~ 21.38816906. Find C(1, 4) + C(3, 4). Give your answer rounded
to 8 digits behind the decimal point in the form ab.cdefghij.