Singular Point
Definition
A point on a curve at which the curve exhibits an unusual behaviour is called a Singular point ( like as point of maxima and minima )
Type of Singular Point
The two main type of singular point is given below.
(I) Multiple point
(II) Point of Inflexion
Multiple point
A point on curve through which more than one branch of curve passes, is called a multiple point of curve .
If two branches of the curve passes through a point, then point on the is known as Double point.
Thus a curve has two tangents at a double point, one for each branch. And these tangents may be real and distinct, real and coincident or imaginary.
Type of Double point
There are three types of double point.
(i) Node
A double point on a curve through which pass two real and distinct tangent, is known as a node.
(ii) Cusp
A double point on a curve through which pass two real and coincident tangent, is known as a cusp.
(iii) Conjugate point or Isolated point
If there are no real points on the curve in the neighbourhood of a point R on the curve then R is called a conjugate point or isolated point
Point of Inflexion
A point where the curve crosses the tangents is called point of inflexion
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