and the line or is tangent to the curve. In this case, if is not 0 then the curve has a point of double contact with If the coefficient of , is 0 but the coefficient of is not then the origin is a point of inflection of the curve. If the coefficients of and are both 0 then the origin is called point of undulation of the curve. This analysis can be applied to any point on the curve by translating the coordinate axes so that the origin is at the given point.

Double points

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