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Let A_1, B_2, C_1, A_2, and B_1 be five points determining a conic. Then the conic is the locus of the point C_2=A_1(L·C_1A_2)·B_1(L·C_1B_2), where L is a line through the ...

Pick any point P on a conic section, and draw a series of right angles having this point as their vertices. Then the line segments connecting the rays of the right angles ...

If S_1, S_2, and S_3 are three conics having the property that there is a point X, not on any of the conics, lying on a common chord of each pair of the three conics (with ...

A curve and its polar reciprocal with regard to the fixed conic have the same Halphen transformation.

A triangle that is equal to its polar triangle with respect to a given conic is said to be self-polar with respect to that conic. Any triangle is self-polar with respect to ...

A point related to the construction and properties of conic sections. Hyperbolas and noncircular ellipses have two distinct foci and two associated conic section directrices, ...

Confocal conics are conic sections sharing a common focus. Any two confocal central conics are orthogonal (Ogilvy 1990, p. 77).

If a triangle is inscribed in a conic section, any line conjugate to one side meets the other two sides in conjugate points.

The distance p (sometimes also denoted k) from the focus to the conic section directrix of a conic section. The following table gives the focal parameter for the different ...

Given a point P, the point P^' which is the antipodal point of P is said to be the antipode of P. The term antipode is also used in plane geometry. Given a central conic (or ...