Find the radius of curvature of the parabola y^2 = 4px at (0,0).
Please teach me how to solve this question. Thank you very much.
In this case take the curvature as:
where we consider as a function of and differentiation is with respect to
This has and interchanged compared to the usual expression but the absolute value of the curvature is the same either way, and this way is easier to handle.
Here:
so:
,
and:
so at , , so:
so the radius of curvature .
RonL