Let us take the arc of a curve and a fixed point

*on it . Now take a variable point*

**P***on the curve and let*

**Q***Then it is definitely ;*

**Q--->P.**

**lim Q-->P(arcPQ/chordPQ)=1****Length of arc as a function :-**

Let

*be the equation of a curve on which we take a fixed point*

**y=f(x)**

**A .**To any given value of

*corresponds a value of*

**x**

**y, viz.,f(x) ;**To that pair of numbers

*and*

**x***corresponds a point*

**f(x)***on the curve, and this point*

**P***has some arcual length*

**P***from*

**s**

**A.**Thus

*is a function of*

**"s"***for the curve*

**x**

**y=f(x)**Similarrly , we can see that

*is a function of parameter*

**"s"***for the curve*

**"t"**

**x=f(t), y=F(t)**------------Parametric Equation

and in function of theta for the curve

**r=f(theta)**------------Polar Equation