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Guilherme Mazui

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What is the Difference Between Parabola and Hyperbola?

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The main difference between a parabola and a hyperbola is their eccentricity, which is a measure of the shape of a conic section. Here are the key differences between parabolas and hyperbolas:

  • Eccentricity: A parabola has an eccentricity of 1, while a hyperbola has an eccentricity greater than 1.
  • Focus and Directrix: A parabola has a single focus and a single directrix, while a hyperbola has two foci and two directrices.
  • Shape: All parabolas have the same shape irrespective of size, while hyperbolas can have different shapes.
  • The Two Arms: In a parabola, the two arms are parallel to each other, while in a hyperbola, the arms open in opposite directions.

In summary, while both parabolas and hyperbolas are conic sections, they differ in their eccentricity, focus, directrix, and shape. A parabola has a single focus and directrix, an eccentricity of 1, and a consistent shape, with two arms that are parallel. In contrast, a hyperbola has two foci and directrices, an eccentricity greater than 1, and varying shapes, with two arms that open in opposite directions.

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  • What is the Difference Between Parabola and Hyperbola?
  • Comparative Table: Parabola vs Hyperbola

    • Comparative Table: Parabola vs Hyperbola

    The main difference between a parabola and a hyperbola is their eccentricity, which is equal to 1 for a parabola and greater than 1 for a hyperbola. Here is a comparison table highlighting the differences between a parabola and a hyperbola:

    Feature Parabola Hyperbola
    Definition Set of points equidistant from a single focus and a directrix Set of points with the difference of distances to two fixed points as a positive constant
    Focus Single focus Two foci
    Directrix Single directrix Two directrices
    Eccentricity E = 1 E > 1
    Shape Symmetrical U-shape, extends infinitely Can be different shapes, two distinct branches never intersect
    Equation y^2 = 4ax (standard form) x^2/a^2 - y^2/b^2 = 1 (standard form)
    Asymptotes None Two asymptotes

    A parabola has a single focus and directrix, and its shape is symmetric, while a hyperbola has two foci and directrices, and its shape can vary. Additionally, a parabola extends infinitely, whereas a hyperbola has two distinct branches that never intersect.

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    Guilherme Mazui

    Guilherme Mazui is graduated in journalism from the Federal University of Minas Gerais (UFMG) and a master's degree in Communication from the University of São Paulo (USP). In addition, he has experience in advertising writing and has worked as a content editor in several companies.