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- Given two pencils of lines at two points and a projective but not perspective mapping of onto , the intersection points of corresponding lines form a non-degenerate projective conic section. (en)
- Let be four points of the parabola , and the intersection of the secant line with the line and let be the intersection of the secant line with the line . Then the secant line is parallel to line . (en)
- Four points with different coordinates are on a parabola with equation if and only if the angles at and have the same measure, as defined above. That is, (en)
- Any parabola is the affine image of the unit parabola with equation . (en)
- Let be given two point sets on two lines , and a projective but not perspective mapping between these point sets, then the connecting lines of corresponding points form a non degenerate dual conic. (en)
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