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As a result of the research project "Strategies for differential calculus meaningful teaching and learning", this paper shows an alternative method to find simplified expressions to determine coordinates and equations for conical sections with focal axis parallel to one coordinated axis by means of implicit derivatives departing from general equation. Unlike other classical methods, and particularly conventional methods used in analytical geometry textbooks, this proposal facilitates conical sections elements and plotting as it does not require algebraic handle of the general equation to convert it to the canonical equation forro. The method shown is easy to systematize from general expressions herein given, expressed in function of the coefficients of the general equation variables in the range of the real numbers.