```I have 6 curve types

![enter image description here][1]

<ul><li>
Type A: If point 1 is positive and point 2 is negative, the curve will not pass through the origin.</li><li>
Type B: If point 1 is negative and point 2 is positive, the curve will pass through the origin twice.</li><li>
Types C-F: If both points are positive or both points are negative, the curve will pass through the origin once.
</li></ul>

The curves are basically partial (and skewed to some degree) [lima&ccedil;ons][2]:

![enter image description here][3]

What **is** known:

<ul><li>
The coordinates of points 1 and 2.</li><li>
The angle of tangents at points 1 and 2.</li><li>
The approximate curve type (lima&ccedil;on).
</li></ul>

What **is not** known:

<ul><li>
The arc length.</li><li>
The degree of skew.
</li></ul>

Data for A-F:

(* A *) {{0.000564367, 0.690525}, {-0.000689501, -0.984192}, 3.03065, -1.95699}
(* B *) {{-0.000689501, -0.984192}, {0.000664785, 1.07289}, -1.95699, 1.82419}
(* C *) {{0.000179304, 1.61576}, {0.0000936314, 0.852042}, 1.15014, 3.52804}
(* D *) {{0.000116063, 0.431337}, {0.000443491, 1.70111}, 2.88997, 1.41834}
(* E *) {{0.0000347276, 0.190688}, {0.000190634, 1.06651}, -3.77228, -2.08792}
(* F *) {{-0.000432719, -1.90935}, {-0.000142565, -0.645011}, -1.36691, -1.927}

in format: `{{point 1}, {point 2}, angle of tangent @ point 1, angle of tangent at point 2}`

Is it possible to estimate a curve fit (and hence arc length & skew) with only the data given?

[1]: http://i.stack.imgur.com/4LV2K.png
[2]: http://en.wikipedia.org/wiki/Lima%C3%A7on
[3]: http://i.stack.imgur.com/cObuQ.png```