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If every diameter is perpendicular to its conjugate, the conic is a circle.

Circle Diameters

If every diameter is perpendicular to its conjugate, the conic is a circle.

Every elliptical involution has the property that there are two definite points in the plane from which any two conjugate points are seen under a right angle.

Circular Involution

Every elliptical involution has the property that there are two definite points in the plane from which…

Any two conjugate diameters of an hyperbola are harmonic conjugates with regard to the asymptotes.

Hyperbola Conjugate Diameters

Any two conjugate diameters of an hyperbola are harmonic conjugates with regard to the asymptotes.