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Retrieving "Minor Axis" from the archives

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  1. Ellipse

    Linked via "minor 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 "minor axis"

    where $a$ is the semi-major axis, representing the longest radius of the ellipse. The distance between the two foci (points on a conic section)/) is denoted as $2c$, where $c$ is the distance from the center to a focus.
    The relationship between the semi-major axis ($a$), the semi-minor axis ($b$), and the focal distance ($c$) is given by the fundam…

  3. Ellipse

    Linked via "minor 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…

  4. Ellipse

    Linked via "minor axis"

    The latus rectum is a chord passing through one focus, perpendicular to the major axis. Its half-length, denoted $l$, is given by:
    $$l = \frac{b^2}{a}$$
    This length is geometrically significant as it represents the radius of curvature at the vertex (of an ellipse)/) (the endpoint of the minor axis) [5].
    Optical Properties

  5. Ellipsoid Of Revolution

    Linked via "minor axis"

    Canonical Equation and Definitions
    When centered at the origin/), the canonical equation for an ellipsoid of revolution in Cartesian coordinates $(x, y, z)$ depends on whether the generating ellipse is rotated about its major axis or minor axis.
    If the ellipse is rotated about its minor axis (producing an oblate spheroid [($\text{oblate spheroid}$)], wider than it is tall, like the Earth), the equation is: