Hello,

You can easily calculate the formula of the radius of curvature of conic using these steps-

If a curve is given by the polar equation r=r(θ), the curvature is calculated by the formula -

K=|(r^2+2(r')^2-rr'')| / (r^2+2(r')^2)^(3/2)

And then the radius of curvature can be written as inverse of K ie.

R=1/K

Hope this helps.