# Tangents and Normals

P(x,y) is any point on the curve f(x,y)=c. PT is tangent at p and PN is **normal** at P. Angle made by tangent PT with x-axis is denoted by in anticlockwise direction.

is defined as slope of gradient of **tangent** PT.

We also define

= slope of *tangent*,

**Slope of normal** =

**Equation of Tangent PT is**

**Equation of normal PN is**

PM is perpendicular from P on x-axis.

By ,

By

**We define:**

**Sub tangent** = TM =

**Sub normal** = MN =

**Length of Tangent** = PT =

**Length of normal** = PN =

Where is point P.

The tangent is parallel to x-axis if:

The tangent is parallel to y â€“axis if:

**Important Note:**

Tangent at the origin is obtained by equating to zero the lowest degree terms, provided the curve passes through origin.

**Definition of Angle of Intersection**

Suppose two curves cut at P. Let be gradient of the two tangents to the two curves at the point of inserction. Angle between the two curves at P is defined as angle between the two tangents at P.

The two curves cut orthogonally if

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