How do you calculate the length of a parabola. The formula would suffice, but the parabola I am tryng to calculate for is symetrical about the y axis, 200mm from one end to the other (as the crow flies) and 91.36mm from the focal point to the x axis. Hope that makes sense.
Thanks.
2007-10-09 03:44:23 · 3 answers · asked by John Sol 4 in Science & Mathematics ➔ Mathematics
The formula for the parabola will be
y = x^2/365.44 (see steve's link)
to find the length of the curve:
integrate 1 + (dy/dx)^2 dx between the limit 0 and 100 and double it
gives the answer 220mm which looks a fair result.
2007-10-09 05:08:06 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Assuming the parabola opens upward: if the vertex is at (0,0), and the distance from the focal point to the vertex is p (so p=91.36 for your case), then the equation of the parabola is
y = x^2/(4p)
Let q be the x-coordinate of the point to the right of the y-axis which is the endpoint of the parabolic arc whose length you want (so in this case q=100). Then the length of the parabolic arc from (-q, q^2/(4p)) to (q, q^2/(4p)) is
2p*[z*sqrt(1 + z^2) + ln(z + sqrt(1 + z^2))]
where z = q/(2p) and ln is natural (base e) log.
2007-10-09 04:56:01 · answer #2 · answered by Anonymous · 0⤊ 0⤋
see wikipedia
Note how, in the first diagram, there is no end to the ends .. so I'm not sure exactly what you are measuring :-)
2007-10-09 04:18:54 · answer #3 · answered by Steve B 7 · 0⤊ 0⤋