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- Proofs_involving_the_ellipse abstract "The derivation of the cartesian form for an ellipse is simple and instructive. One simple definition of the ellipse is the "locus of all points of the plane whose distances to two fixed points(called the foci) add to the same constant". See ellipse for other definitions.Let the foci be points (-c,0) and (c,0). Then the ellipse center is (0, 0).If (x,y) is any point on the ellipse and if is the distance between (x,y) and (-c,0) and is the distance between (x,y) and (c,0), i.e.File:Ellipse derivation 1.svgthen we can define (a here is the semi-major axis, although this is irrelevant for the sake of the proof). From this simple definition we can derive the cartesian equation. Substituting:To simplify we isolate the radical and square both sides.Solving for the root and simplifying:Swap sides to return to original format and continue:A final squaringGrouping the x-terms and dividing by Where: If x = 0 then (where b is the semi-minor axis)Therefore we can substituteAnd we have our desired equation:".
- Proofs_involving_the_ellipse thumbnail Ellipse_derivation_1.svg?width=300.
- Proofs_involving_the_ellipse wikiPageID "1697582".
- Proofs_involving_the_ellipse wikiPageRevisionID "604314839".
- Proofs_involving_the_ellipse hasPhotoCollection Proofs_involving_the_ellipse.
- Proofs_involving_the_ellipse subject Category:Article_proofs.
- Proofs_involving_the_ellipse subject Category:Conic_sections.
- Proofs_involving_the_ellipse type Abstraction100002137.
- Proofs_involving_the_ellipse type ArticleProofs.
- Proofs_involving_the_ellipse type Attribute100024264.
- Proofs_involving_the_ellipse type Cognition100023271.
- Proofs_involving_the_ellipse type ConicSection113872975.
- Proofs_involving_the_ellipse type ConicSections.
- Proofs_involving_the_ellipse type Evidence105823932.
- Proofs_involving_the_ellipse type Figure113862780.
- Proofs_involving_the_ellipse type Information105816287.
- Proofs_involving_the_ellipse type PlaneFigure113863186.
- Proofs_involving_the_ellipse type Proof105824739.
- Proofs_involving_the_ellipse type PsychologicalFeature100023100.
- Proofs_involving_the_ellipse type Shape100027807.
- Proofs_involving_the_ellipse comment "The derivation of the cartesian form for an ellipse is simple and instructive. One simple definition of the ellipse is the "locus of all points of the plane whose distances to two fixed points(called the foci) add to the same constant". See ellipse for other definitions.Let the foci be points (-c,0) and (c,0).".
- Proofs_involving_the_ellipse label "Proofs involving the ellipse".
- Proofs_involving_the_ellipse sameAs m.05p6wv.
- Proofs_involving_the_ellipse sameAs Q7250028.
- Proofs_involving_the_ellipse sameAs Q7250028.
- Proofs_involving_the_ellipse sameAs Proofs_involving_the_ellipse.
- Proofs_involving_the_ellipse wasDerivedFrom Proofs_involving_the_ellipse?oldid=604314839.
- Proofs_involving_the_ellipse depiction Ellipse_derivation_1.svg.
- Proofs_involving_the_ellipse isPrimaryTopicOf Proofs_involving_the_ellipse.
