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  2. Conic section - Wikipedia

    en.wikipedia.org/wiki/Conic_section

    The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though it was sometimes called as a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga 's systematic work on their properties.

  3. Confocal conic sections - Wikipedia

    en.wikipedia.org/wiki/Confocal_conic_sections

    (The parabolas are orthogonal for an analogous reason to confocal ellipses and hyperbolas: parabolas have a reflective property.) Analogous to confocal ellipses and hyperbolas, the plane can be covered by an orthogonal net of parabolas, which can be used for a parabolic coordinate system .

  4. Triangle conic - Wikipedia

    en.wikipedia.org/wiki/Triangle_conic

    Other examples are the Steiner ellipse, which is an ellipse passing through the vertices and having its centre at the centroid of the reference triangle; the Kiepert hyperbola which is a conic passing through the vertices, the centroid and the orthocentre of the reference triangle; and the Artzt parabolas, which are parabolas touching two ...

  5. Focal conics - Wikipedia

    en.wikipedia.org/wiki/Focal_conics

    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 the hyperbola are the foci of the ellipse and its foci are the ...

  6. Matrix representation of conic sections - Wikipedia

    en.wikipedia.org/wiki/Matrix_representation_of...

    A parabola, being tangent to the line at infinity, would have its center being a point on the line at infinity. Hyperbolas intersect the line at infinity in two distinct points and the polar lines of these points are the asymptotes of the hyperbola and are the tangent lines to the hyperbola at these points of infinity.

  7. Hyperbola - Wikipedia

    en.wikipedia.org/wiki/Hyperbola

    A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows. The hyperbola is one of the three kinds of conic section, formed by the intersection of a plane and a double cone. (The other conic sections are the parabola and the ellipse. A circle is a special case of an ...

  8. Circumconic and inconic - Wikipedia

    en.wikipedia.org/wiki/Circumconic_and_inconic

    Incircle, the unique circle that is internally tangent to a triangle's three sides; Steiner inellipse, the unique ellipse that is tangent to a triangle's three sides at their midpoints; Mandart inellipse, the unique ellipse tangent to a triangle's sides at the contact points of its excircles; Kiepert parabola; Yff parabola

  9. List of curves - Wikipedia

    en.wikipedia.org/wiki/List_of_curves

    This page was last edited on 2 December 2024, at 16:34 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.

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