algebra output of ellipse(focus1,focus2,point) and hyperbola(focus1,focus2,point)
Hi everybody, when there is a distance of irrational length involved, the coefficients in the corresponding equations shown in the algebra window are too large by a factor of 16. For example, ELLI1=ellipse((-4,0),(4,0),(0,3)) correctly yields 9*x^2 + 25*y^2 = 225, but ELLI2=ellipse((-4,0),(4,0),(6,4)) yields 673.33*x^2 + 929.33 * y^2 = 39109.21 . The command SemiMajorAxisLength(ELLI2) yields 7.62, the square of which is 58.08. 929.33/58.08 = 16.00... the equation is correct, of course, but the coefficients cannot be interpreted as squared semi-axes. Same effect occurs for command hyperbola, and moreover, for a vertically open hyperbola, in order to obtained the canonical form, a factor of -1 has to be applied to the equation. GeoGebra Classic 5.4.927.1-d