In general, if given equation of any two curves, how to find the shortest distance?
According to me, finding common normal won't work as it isn't necessary for both of them to have one like in case of domain bounded functions.
We can take a more general approach i.e. by assuming points on both the curves, forming the expression for distance between the points and then minimizing it using partial derivatives.
Though the latter approach is reliable but too lengthy and many a times it produces equations quite difficult to solve especially in case of conics. Isn't there a better method?