If a one-parameter family of curves has index and class , the number tangent to a curve of order and class in general position is
Chasles's Contact Theorem
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References
Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 436, 1959.Referenced on Wolfram|Alpha
Chasles's Contact TheoremCite this as:
Weisstein, Eric W. "Chasles's Contact Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ChaslessContactTheorem.html