How to find the length of the arc (which is the part of a parabola) formed between the points (-b,0) and (b,0) with the point on it, (0,a) in contact with the y axis?

06-Oct-2015 6:19 PM

Answers (2)


For a parabola with :

Arc length can be calculated by solving :

By integrating and solving this, we get:

Using this formulla and we can find arc length for the parabola you asked for:

by subsituting 

a = b

h = a

We get:

Integration ( b2 + 4 * a )1/2 + b2/2*a sinh-1(2 * a/b)

06-10-2015 18:52



The length of parabolic arc from 'a' to 'b' is calculated using integration of √( 1+[f ′(x)]2  ) from a to b.

[ f ′(x)  = derivative of f(x) ]

L = ∫ √( 1+[f ′(x) ])dx

Integrate from a to b. ( In your case '-b' to 'b' )


06-10-2015 19:09

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