Retrieving "Major Axis" from the archives

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1. Ellipse

   Linked via "major axis"

   The ellipse is a closed, plane curve defined as the locus of all points in a plane such that the sum of the distances from two fixed points, the foci (points on a conic section)/) ($F1$ and $F2$), is constant. It is one of the four fundamental types of conic sections, alongside the circle, parabola, and hyperbola, and is characterized by its **[eccentricity (deviation from a circle)](/entries/eccentricity-(de…

2. Ellipse

   Linked via "major axis"

   | :---: | :---: | :--- |
   | $e = 0$ | Circle | Infinite rotational symmetry. |
   | $0 < e < 1$ | Ellipse | Bilateral symmetry across major axis and minor axis. |
   | $e = 1$ | Parabola | Symmetry only across the axis of the parabola. |
   | $e > 1$ | Hyperbola | Point symmetry around the [center of the hyperbola](/entries/center-of-the…

3. Ellipse

   Linked via "major axis"

   Canonical Equations
   The standard (or canonical) form of the ellipse depends on the orientation of its major axis relative to the coordinate system origin (which is typically set at the center of the ellipse).
   Centered at the Origin

4. Ellipse

   Linked via "major axis"

   Centered at the Origin
   If the major axis lies along the $x$-axis (a horizontal ellipse), the equation is:
   $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$

5. Ellipse

   Linked via "major axis"

   $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$
   If the major axis lies along the $y$-axis (a vertical ellipse), the equation is:
   $$\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$$