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  2. Parabola - Wikipedia

    en.wikipedia.org/wiki/Parabola

    Suppose a system of Cartesian coordinates is used such that the vertex of the parabola is at the origin, and the axis of symmetry is the y axis. The parabola opens upward. It is shown elsewhere in this article that the equation of the parabola is 4fy = x 2, where f is the focal length.

  3. Quadrature of the Parabola - Wikipedia

    en.wikipedia.org/wiki/Quadrature_of_the_Parabola

    A parabolic segment is the region bounded by a parabola and line. To find the area of a parabolic segment, Archimedes considers a certain inscribed triangle. The base of this triangle is the given chord of the parabola, and the third vertex is the point on the parabola such that the tangent to the parabola at that point is parallel to the chord.

  4. Confocal conic sections - Wikipedia

    en.wikipedia.org/wiki/Confocal_conic_sections

    A parabola has only one focus, and can be considered as a limit curve of a set of ellipses (or a set of hyperbolas), where one focus and one vertex are kept fixed, while the second focus is moved to infinity. If this transformation is performed on each conic in an orthogonal net of confocal ellipses and hyperbolas, the limit is an orthogonal ...

  5. Focal conics - Wikipedia

    en.wikipedia.org/wiki/Focal_conics

    A: vertex of the red parabola and focus of the blue parabola F: focus of the red parabola and vertex of the blue parabola. In geometry, focal conics are a pair of curves consisting of [1] [2] either an ellipse and a hyperbola, where the hyperbola is contained in a plane, which is orthogonal to the plane containing the ellipse. The vertices of ...

  6. Conic section - Wikipedia

    en.wikipedia.org/wiki/Conic_section

    Define b by the equations c 2 = a 2 − b 2 for an ellipse and c 2 = a 2 + b 2 for a hyperbola. For a circle, c = 0 so a 2 = b 2, with radius r = a = b. For the parabola, the standard form has the focus on the x-axis at the point (a, 0) and the directrix the line with equation x = −a. In standard form the parabola will always pass through the ...

  7. Semi-major and semi-minor axes - Wikipedia

    en.wikipedia.org/wiki/Semi-major_and_semi-minor_axes

    Note that for a given amount of total mass, the specific energy and the semi-major axis are always the same, regardless of eccentricity or the ratio of the masses. Conversely, for a given total mass and semi-major axis, the total specific orbital energy is always the same. This statement will always be true under any given conditions. [citation ...

  8. RFK Jr set to face abortion, vaccine scrutiny in sit-downs ...

    www.aol.com/rfk-jr-set-face-abortion-090044444.html

    Trump HHS Secretary nominee Robert F. Kennedy Jr. will face questions on several controversial topics from senators when he makes the rounds on Capitol Hill this week.

  9. Eccentricity (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Eccentricity_(mathematics)

    A family of conic sections of varying eccentricity share a focus point and directrix line, including an ellipse (red, e = 1/2), a parabola (green, e = 1), and a hyperbola (blue, e = 2). The conic of eccentricity 0 in this figure is an infinitesimal circle centered at the focus, and the conic of eccentricity ∞ is an infinitesimally separated ...