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From: Ken on 4 Jun 2010 17:09 If a parabola y = ax^2 + bx + c is rotated through an angle t, how can one determine the corresponding coefficients of the general parabola Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, where B^2 = 4AC? Also, the reverse question, given the coefficients of a general parabola, how to find the coefficients of the 'normal' parabola and angle t? I know it can be done numerically using curve fitting techniques (e.g. least squares), but I was hoping for a more elegant (analytical/ algebraic) approabh. Any ideas?
From: Philippe 92 on 5 Jun 2010 03:50 Ken wrote : > If a parabola y = ax^2 + bx + c is rotated through an angle t, how can > one determine the corresponding coefficients of the general parabola > Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, where B^2 = 4AC? Also, the > reverse question, given the coefficients of a general parabola, how to > find the coefficients of the 'normal' parabola and angle t? > > I know it can be done numerically using curve fitting techniques (e.g. > least squares), but I was hoping for a more elegant (analytical/ > algebraic) approabh. Any ideas? See Tim Walter's thread Subject: Rotation question Date: Thu, 18 Mar 2010 14:25:56 -0000 Message-ID: <3jq2mq.jqq.17.1(a)news.alt.net> Regards. -- Philippe C., mail : chephip, with domain free.fr site : http://mathafou.free.fr/ (mathematical recreations)
From: Han de Bruijn on 5 Jun 2010 06:43
On 5 jun, 09:50, "Philippe 92" <nos...(a)free.invalid> wrote: > Ken wrote : > > > If a parabola y = ax^2 + bx + c is rotated through an angle t, how can > > one determine the corresponding coefficients of the general parabola > > Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, where B^2 = 4AC? Also, the > > reverse question, given the coefficients of a general parabola, how to > > find the coefficients of the 'normal' parabola and angle t? > > > I know it can be done numerically using curve fitting techniques (e.g. > > least squares), but I was hoping for a more elegant (analytical/ > > algebraic) approabh. Any ideas? > > See Tim Walter's thread > Subject: Rotation question > Date: Thu, 18 Mar 2010 14:25:56 -0000 > Message-ID: <3jq2mq.jqq.17.1(a)news.alt.net> > > Regards. > > -- > Philippe C., mail : chephip, with domain free.fr > site :http://mathafou.free.fr/ (mathematical recreations) http://groups.google.nl/group/sci.math/msg/e4c268fc2e896686 http://groups.google.nl/group/sci.math/msg/761fba59b17bc5cd Han de Bruijn |