The implicit equation $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is correctly plotted as an ellipse. Subtracting $\frac{x^2}{a^2}$ should not change the plot, however, $\frac{y^{2}}{b^{2}}=1-\frac{x^{2}}{a^{2}}$ is plotted as a hyperbola. For good measure I have thrown in further transformations of the equation (making it an explicit equation); they are displayed correctly.
Vice versa, the equation $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is correctly plotted as a hyperbola but the transformed equation $\frac{x^2}{a^2}=1+\frac{y^2}{b^2}$ becomes an ellipse (not shown in image).
alexhuntley
commented
1 year ago
The implicit equation $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is correctly plotted as an ellipse. Subtracting $\frac{x^2}{a^2}$ should not change the plot, however, $\frac{y^{2}}{b^{2}}=1-\frac{x^{2}}{a^{2}}$ is plotted as a hyperbola. For good measure I have thrown in further transformations of the equation (making it an explicit equation); they are displayed correctly.
Vice versa, the equation $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is correctly plotted as a hyperbola but the transformed equation $\frac{x^2}{a^2}=1+\frac{y^2}{b^2}$ becomes an ellipse (not shown in image).