Arcs and Chords

 


Let us take the arc of a curve and a fixed point   P  on it . Now take a variable point   Q   on the curve and let    Q--->P.     Then it is definitely ;

lim Q-->P(arcPQ/chordPQ)=1


Length of arc as a function :- 

Let    y=f(x)   be the equation of a curve on which we take a fixed point    A   .

To any given value of   x   corresponds a value of

  y, viz.,f(x) ;

To that pair of numbers   x    and   f(x)   corresponds a point    P   on the curve, and this point  P   has some arcual length   s    from   A.  

 Thus   "s"   is a function of   x   for the curve

y=f(x)

Similarrly , we can see that   "s"   is a function of parameter   "t"   for the curve

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

and in function of   theta   for the curve

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