Revision #776 → #1179 · back to history
addedEllipse (locus definition)7cdb28fd0cdf
addedEccentricity of an ellipse97e884c1b7f6
addedStandard equation of an ellipse41951163801a
addedEllipse as conic section0718e3a6fce2
addedFocus-directrix definition of ellipse5e721c05a122
addedCenter, axes, vertices, focal distance, eccentricity5b385fcef4b4
addedCircle as special ellipsed07c35d1b7fb
addedCircular directrixd5f71f2bc809
addedDandelin spheres: conic section is ellipsed26f49287409
addedStandard form coordinates of ellipse818f2bcbd625
addedDerivation of standard ellipse equationc3d5cc615cb3
addedSemi-major and semi-minor axes, co-vertices58eecf00de19
addedSymmetry of the ellipse47ae431dfd4c
addedPrincipal axes conventionbb416c5b2edc
addedLinear eccentricityfc4dcbaddadd
addedEccentricity formula6b5f160ba132
addedZero-eccentricity circlef3eb87d5aa0d
addedLatus rectum and semi-latus rectum0b6d974e26c4
addedSemi-latus rectum equals radius of curvature at vertex77426854cbc7
addedExterior line, tangent, secant1da60999dcdc
addedTangent equation at point on ellipse05b08cab4c47
addedConjugate diameters criterionc584080bd082
addedShifted ellipse equation279afb805624
addedGeneral ellipse as quadric34c126fb2f00
addedNon-degeneracy criterion via determinantd50f75980f0f
addedGeneral-form coefficients from canonical parameters38c2536503aa
addedCanonical parameters from general-form coefficientsd4c62768d0e7
addedStandard parametric representationf587c1df2fbb
addedEccentric anomalyd9ae15dd2bdb
addedRational parametric equation of ellipse6a2e3afcbeed
addedProjective-line rational parametrization23422818f806
addedTangent-slope parametric representationfcb6bf2d007e
addedTangent equation via slope parametercbbf345ca945
addedEllipse as affine image of unit circle800118f3354e
addedVertices of affine-image ellipseaf8d98ef3fab
addedArea from Apollonios theoremf7a69f7b300a
addedSemiaxes from conjugate-diameter system8220aaedcd3f
addedImplicit representation via Cramer's rulebdf4d5465002
addedConjugate diameters from equation931f5eca5402
addedPolar form relative to centere60067107fea
addedPolar form relative to focusfd602b6d5fc2
addedTrue anomaly9d597e5f9c48
addedDirectrix of ellipse05a1042e33fe
addedFocus-directrix ratio equals eccentricity469e25b44440
addedConverse focus-directrix definition53313e29e220
addedConic classification by eccentricity162bc6cafd65
addedDirectrix-focus inversion construction7374db5dfbee
addedFocus-to-focus reflection property45f37ab2f943
addedReflection of rays to second focuse6fcfb460120
addedAlignment with major axis5d04696c2421
addedMidpoints of parallel chords on a diameter (circle)ec81dac7aca6
addedConjugate diameters of an ellipsea2f8267e4f73
addedConjugate diameters via parallel tangents99de21c0efbd
addedApollonios's theorem on conjugate diameters5de43fca0f9f
addedOrthoptic / director circleb7fd86df64dc
addedde La Hire's point construction0cf7a58b7ac7
addedPins-and-string locus method2374456cd622
addedPaper strip method (first)27119b6f0bab
addedPaper strip method (second)025faa956821
addedRadius of curvature at vertices and co-vertices070f3627a879
addedSteiner generation of conic27c3fc5ca22f
addedEllipse as hypotrochoid (Tusi couple)81d9c59cb1e0
addedCircle determined by three non-collinear points049a9a65eeb4
addedInscribed angle theorem for circles9afcf7ea9d30
addedThree-point form of circle equationec759174afe6
addedEllipse determined by three points (family of fixed eccentricity)89b86c1d9d9d
addedInscribed angle theorem for ellipsesc37f7d3ae90c
addedThree-point form of ellipse equationeea752d9f9bf
addedPole-polar relation5ba1e9ba20bd
addedProperties of pole-polar relationf6f90be828cd
addedIntersection of polars is pole of line through poles5af80b1d67d0
addedFoci and directrices as pole-polar pairsf7e758790941
addedArea enclosed by ellipse6288a9dbfaf0
addedArea of implicit ellipse47f9074b7140
addedArea in terms of eccentricityc659341e752c
addedArea of tilted ellipseb206a6b35db8
addedCircumference of ellipse809bd0221ae8
addedInfinite series for circumference5c081edf6661
addedIvory/Bessel/Kummer rapidly converging series24843d7da95d
addedRamanujan approximations for circumferencedd996b5af63a
addedArc length via incomplete elliptic integral2b625b5e0841
addedBounds on circumference2fbc5c108947
addedCurvature and radius of curvaturef851132501e6
addedRadius of curvature as function of anglea59185d81be8
addedEvolute is an astroid87d7c61186a9
addedSteiner ellipse and inellipsescfa036f88b6f
addedEllipses as plane sections of quadrics4589f5f741b1
addedKepler's first lawa5531aba4f27
addedElliptical orbit relations25fa6a8b4308
addedMeans of apoapsis and periapsis663e883039ac
addedHarmonic oscillator orbit is ellipse935c96082291
addedElliptically distributed random vector77a807ac55f7