The path of an ellipse is the length of the line segment obtained by the intersection of a straight line perpendicular to the long axis and the ellipse.

So use c instead of x in the elliptic equation,

Y 1 = b 2/a and y2 =-b/a can be obtained.

So the length of the path is y1-y2 = 2b 2/a.

Where b 2 stands for the square of B.