Thread: Curvature of implicit equation

Hi,

I need to find the curvature k of y=sqrt(R^2 - x^2)

I know k = |f''| / (1 + f' ^2) ^1.5

But I think I have gone somewhere with my differentiation as I didn't end up with k = 1/R which is the answer :/

Thanks in advance for the help.

Originally Posted by PStudent175

Hi,

I need to find the curvature k of y=sqrt(R^2 - x^2)

I know k = |f''| / (1 + f' ^2) ^1.5

But I think I have gone somewhere with my differentiation as I didn't end up with k = 1/R which is the answer :/

Thanks in advance for the help.

clean up the algebra ...

Sorry how did you get y' = -x/y ?

I got y' = f' = -x(R^2 - x^2)^-0.5 from the chain rule

implicit derivative ...

... note that is a constant

Ok great thanks, could you also show how you got y'' = -R^2 / y^3 ?

quotient rule ...







multiply numerator and denominator by to clear the complex fraction ...