Hey M.R.
The parametricform of the evolute is given on that page in the second pair of formulas since you have the same form as your question gives.
Hi,
I am trying to solve the following question:
For the plane curve , find a parametric equation of its evolute.
I looked at this website: Parabola Evolute -- from Wolfram MathWorld
From there I get the cartesian equation? Is there a general formula for evolute? I am not sure which equation to use from Evolute - Wikipedia, the free encyclopedia . Can someone point me in the right direction? Thanks
For that one yes, (since a = 1) since it has the same functional form.
There is a link on that page that takes you to this:
Evolute -- from Wolfram MathWorld
It outlines how to get the non-parametric form for the evolute, but be aware that if it's only y in terms of x, all you have to do is let x = t and y = f(t) to get a parametric form of the equation (in other words, x = t and y = whatever the final function is given by that formula which are just functions of t).
When I say the above I don't mean the final x value will be t: only the intermediate value within the functions. For example if the original curve is y = x^3 - x^2 + 5x^4, then x = t and y = f(x) = f(t) but for the final involute you will have combinations of f(t), g(t) and its derivatives which will give you a complex parametrization for your evolute x(t) and y(t).