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The linear eccentricity ($c$) of an ellipse, which is the distance from the center to each focus, is used in trigonometry to derive the equation of an ellipse in terms of its foci.

The focal length ($p$) of a parabola is utilized in trigonometry to find the focus and to determine the steepness and direction of the parabola.

These axes' lengths are used in trigonometry to write the hyperbola's equation and to calculate the coordinates of its vertices and foci.

The directrix of a parabola is a line used in trigonometry to help determine the set of points equidistant from the focus and the directrix itself.

Eccentricity ($e$) defines the shape of an ellipse and is used in trigonometry to locate a point on the ellipse using the focus and the directrix.

In a hyperbola, the eccentricity ($e$) is greater than 1, and trigonometry can be applied to calculate the distance between a point on the hyperbola and the foci.

The axes of symmetry in conic sections are lines that can be used with trigonometry to reflect points across the axis and to help derive the standard equations of conic sections.