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Remark 1: The 2-points–2-tangents property of a parabola is an affine version of the 3-point degeneration of Pascal's theorem. Remark 2: The 2-points–2-tangents property should not be confused with the following property of a parabola, which also deals with 2 points and 2 tangents, but is not related to Pascal's theorem.
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.
This also works the other way around: a parallel beam of light that is parallel to the axis of the paraboloid is concentrated at the focal point. For a proof, see Parabola § Proof of the reflective property. Therefore, the shape of a circular paraboloid is widely used in astronomy for parabolic reflectors and parabolic antennas.
A conic is the curve obtained as the intersection of a plane, called the cutting plane, with the surface of a double cone (a cone with two nappes).It is usually assumed that the cone is a right circular cone for the purpose of easy description, but this is not required; any double cone with some circular cross-section will suffice.
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 ...
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Malcolm X was assassinated in 1965 when gunmen opened fire while he gave a speech in New York. A new lawsuit accuses the government of conspiracy.
Regardless of the format, the graph of a univariate quadratic function () = + + is a parabola (as shown at the right). Equivalently, this is the graph of the bivariate quadratic equation = + +. If a > 0, the parabola opens upwards. If a < 0, the parabola opens downwards.