MHB How Do You Calculate the Radius of Curvature for Complex Curves?

[abhik5195]

1) Find the radius of curvature at any point of the cycloid x = a(\theta + sin\theta)y = a(1- cos\theta).
2) Find the radius of curvature at the point (3a/2 , 3a/2) for the curve x³ + y³ = 3axy

 

[HallsofIvy]

What do you mean by "help"? Do your homework for you? It is impossible to actually help without knowing what you do understand and what you can do yourself. Do you know what "radius of curvature" means? Do you know how to find the curvature of a one dimensional curve? Have you not at least attempted to do this problem yourself?

Does your textbook give no formulas for "radius of curvature"? Did you "google" "radius of curvature"? When I did I got https://en.wikipedia.org/wiki/Radius_of_curvature
which seems to be exactly what you need.