## 6

## Tangents and Normals

##### 6.1 INTRODUCTION

We know that a *tangent line* to a curve *C* at a point *P* is the line, in the limiting position, if it exists, of the secant through the point *P* and a variable point *Q* on *C* as *Q* moves along *C* closer to *P*. Also we know that the slope of tangent to the curve *y* = *f* (*x*) at (*x*, *y*) is *f* ′(*x*).

In the figure above, the line *P T* is tangent to the curve at *P*, *T R* is called *sub-tangent* and *RM* is called *sub – normal*.

##### 6.2 EQUATION OF THE TANGENT AT A POINT OF A CURVE

Let *P*(*x*_{1}, *y*_{1}) be a point in a curve *C*. Then equation of a line passing through *P*(*x*_{1}, *y*_{1}) and with slope *m* is given by

*y*–

*y*

_{1}=

*m*(

*x*–

*x*

_{1}),

where

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