# Problem 404: Crisscross Ellipses

![graphic](img404.gif)

Ea is an ellipse with an equation of the form x2 + 4y2 = 4a2. Ea' is the
rotated image of Ea by θ degrees counterclockwise around the origin O(0,
0) for 0° < θ < 90°. b is the distance to the origin of the two
intersection points closest to the origin and c is the distance of the
two other intersection points. We call an ordered triplet (a, b, c) a
canonical ellipsoidal triplet if a, b and c are positive integers. For
example, (209, 247, 286) is a canonical ellipsoidal triplet. Let C(N) be
the number of distinct canonical ellipsoidal triplets (a, b, c) for a ≤
N. It can be verified that C(103) = 7, C(104) = 106 and C(106) = 11845.
Find C(1017).