Ellipse Catacaustic

For an ellipse given by the parametric equations

			(1)
			(2)

the catacaustic is a complicated expression for generic radiant point . However, it simplifies for a number of special cases to

			(3)
			(4)

for (0, 0),

			(5)
			(6)

for , and

			(7)
			(8)

for .