The points of intersection of asymptotes of a hyperbola with directrices lies on

• Asymptotes of a hyperbola are the diagonals of the rectangle formed by the lines drawn through the extremities of each axis parallel to the other axis.
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• A perpendicular drawn from the foci on either asymptote meet it in the same points as the corresponding directrix and the common points of intersection lie on the auxiliary circle

point of intersection of asymptotes of a hyperbola with directrices lies on Auxiliary circle.