Assertion: ellipse's diameter | /r/HasProperty | conjugate
Facets:
value: to its reflection in the asymptote
type: TRANSITIVE-OBJECT
value: if
type: DEGREE
value: for any φ
type: OTHER
value: for an ellipse
type: PURPOSE
Source sentences:
text: Two diameters d 1 , d 2 {\displaystyle d_{1},\,d_{2}} of an ellipse are conjugate if the midpoints of chords parallel to d 1 {\displaystyle d_{1}} lie on d 2 . {
text: For example, two diameters of a circle are conjugate if and only if they are perpendicular.
text: For an ellipse, two diameters are conjugate if and only if the tangent line to the ellipse at an endpoint of one diameter is parallel to the other diameter.
text: For any φ, the indicated diameters of the circles and hyperbolas are conjugate.
text: Similar to the elliptic case, diameters of a hyperbola are conjugate when each bisects all chords parallel to the other.
text: A diameter of one hyperbola is conjugate to its reflection in the asymptote, which is a diameter of the other hyperbola.