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    Geometria Analítica : rotação e translação de eixos coordenados
    (2026-04-27) Saavedra, Beto
    Rotation and translation of coordinate axes are fundamental techniques in Analytic Geometry used to simplify equations. The equation xy-x+y-3=0 represents a hyperbola. The mixed term (xy) indicates that the curve is not aligned with the original coordinate axes. For this reason, we apply a rotation of the axes by an angle (\theta) in order to eliminate the mixed term and obtain a simpler form of the equation. After the rotation, a translation of the axes may also be performed, shifting the origin to the center of the curve. In this way, the canonical form of the hyperbola is obtained. The change of coordinates makes it possible to: * identify the type of conic; * find the center of the curve; * determine symmetries; * facilitate the calculation of geometric elements such as vertices, foci, and asymptotes. The video allows us to visualize dynamically the harmony between the rotated axes (x_1) and (y_1), the angle (\theta), and the equations representing the hyperbola throughout the geometric transformation.