This article studies two methods for finding the stress equation for second-order lines - a geometric method based on the limit state of the cutting line and a differential method based on the geometric meaning of the derivative. The theoretical foundations of both methods are explained, and the process of deriving the stress equation is analyzed in detail. Based on the results obtained, the similarities and differences, advantages, and application possibilities of the methods are compared. As a result of the study, it was shown that both methods lead to the same stress equation, but differ in computational convenience and theoretical approach.