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- https://math.libretexts.org/Courses/Lorain_County_Community_College/Book%3A_Precalculus_Jeffy_Edits_3.75/07%3A_Hooked_on_Conics/7.04%3A_EllipsesWe may imagine taking a length of string and anchoring it to two points on a piece of paper. The curve traced out by taking a pencil and moving it so the string is always taut is an ellipse.
- https://math.libretexts.org/Workbench/MAT_2420_Calculus_II/07%3A_Parametric_Equations_and_Polar_Coordinates/7.06%3A_Conic_SectionsConic sections get their name because they can be generated by intersecting a plane with a cone. A cone has two identically shaped parts called nappes. Conic sections are generated by the intersection...Conic sections get their name because they can be generated by intersecting a plane with a cone. A cone has two identically shaped parts called nappes. Conic sections are generated by the intersection of a plane with a cone. If the plane is parallel to the axis of revolution (the y-axis), then the conic section is a hyperbola. If the plane is parallel to the generating line, the conic section is a parabola. If the plane is perpendicular to the axis of revolution, the conic section is a circle.
- https://math.libretexts.org/Courses/Mission_College/Math_3B%3A_Calculus_2_(Sklar)/11%3A_Parametric_Equations_and_Polar_Coordinates/11.05%3A_Conic_SectionsConic sections get their name because they can be generated by intersecting a plane with a cone. A cone has two identically shaped parts called nappes. Conic sections are generated by the intersection...Conic sections get their name because they can be generated by intersecting a plane with a cone. A cone has two identically shaped parts called nappes. Conic sections are generated by the intersection of a plane with a cone. If the plane is parallel to the axis of revolution (the y-axis), then the conic section is a hyperbola. If the plane is parallel to the generating line, the conic section is a parabola. If the plane is perpendicular to the axis of revolution, the conic section is a circle.
- https://math.libretexts.org/Courses/Lorain_County_Community_College/Book%3A_Precalculus_(Stitz-Zeager)_-_Jen_Test_Copy/07%3A_Hooked_on_Conics/7.04%3A_EllipsesWe may imagine taking a length of string and anchoring it to two points on a piece of paper. The curve traced out by taking a pencil and moving it so the string is always taut is an ellipse.
- https://math.libretexts.org/Courses/Mission_College/MAT_3B_Calculus_II_(Kravets)/11%3A_Parametric_Equations_and_Polar_Coordinates/11.01%3A_Conic_SectionsConic sections get their name because they can be generated by intersecting a plane with a cone. A cone has two identically shaped parts called nappes. Conic sections are generated by the intersection...Conic sections get their name because they can be generated by intersecting a plane with a cone. A cone has two identically shaped parts called nappes. Conic sections are generated by the intersection of a plane with a cone. If the plane is parallel to the axis of revolution (the y-axis), then the conic section is a hyperbola. If the plane is parallel to the generating line, the conic section is a parabola. If the plane is perpendicular to the axis of revolution, the conic section is a circle.
- https://math.libretexts.org/Workbench/College_Algebra_2e_(OpenStax)/08%3A_Analytic_Geometry/8.02%3A_The_EllipseThe key features of the ellipse are its center, vertices, co-vertices, foci, and lengths and positions of the major and minor axes. Just as with other equations, we can identify all of these features ...The key features of the ellipse are its center, vertices, co-vertices, foci, and lengths and positions of the major and minor axes. Just as with other equations, we can identify all of these features just by looking at the standard form of the equation. There are four variations of the standard form of the ellipse. These variations are categorized first by the location of the center (the origin or not the origin), and then by the position (horizontal or vertical). Each is presented here.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus_II__Integral_Calculus_._Lockman_Spring_2024/06%3A_Parametric_Equations_and_Polar_Coordinates/6.05%3A_Conic_SectionsConic sections get their name because they can be generated by intersecting a plane with a cone. A cone has two identically shaped parts called nappes. Conic sections are generated by the intersection...Conic sections get their name because they can be generated by intersecting a plane with a cone. A cone has two identically shaped parts called nappes. Conic sections are generated by the intersection of a plane with a cone. If the plane is parallel to the axis of revolution (the y-axis), then the conic section is a hyperbola. If the plane is parallel to the generating line, the conic section is a parabola. If the plane is perpendicular to the axis of revolution, the conic section is a circle.
- https://math.libretexts.org/Bookshelves/Calculus/Elementary_Calculus_2e_(Corral)/07%3A_Analytic_Geometry_and_Plane_Curves/7.01%3A_EllipsesIn the \(xy\)-plane, let the foci of an ellipse be the points \((\pm c,0)\) for some \(c>0\), so that the center is the origin \((0,0)\) and the \(x\)-axis is the principal axis, as in the figure on t...In the \(xy\)-plane, let the foci of an ellipse be the points \((\pm c,0)\) for some \(c>0\), so that the center is the origin \((0,0)\) and the \(x\)-axis is the principal axis, as in the figure on the right.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/09%3A_Curves_in_the_Plane/9.01%3A_Conic_SectionsThe ancient Greeks recognized that interesting shapes can be formed by intersecting a plane with a double napped cone (i.e., two identical cones placed tip--to--tip as shown in the following figures)....The ancient Greeks recognized that interesting shapes can be formed by intersecting a plane with a double napped cone (i.e., two identical cones placed tip--to--tip as shown in the following figures). As these shapes are formed as sections of conics, they have earned the official name "conic sections.''
- https://math.libretexts.org/Workbench/Algebra_and_Trigonometry_2e_(OpenStax)/12%3A_Analytic_Geometry/12.02%3A_The_EllipseThe key features of the ellipse are its center, vertices, co-vertices, foci, and lengths and positions of the major and minor axes. Just as with other equations, we can identify all of these features ...The key features of the ellipse are its center, vertices, co-vertices, foci, and lengths and positions of the major and minor axes. Just as with other equations, we can identify all of these features just by looking at the standard form of the equation. There are four variations of the standard form of the ellipse. These variations are categorized first by the location of the center (the origin or not the origin), and then by the position (horizontal or vertical). Each is presented here.
- https://math.libretexts.org/Courses/Northeast_Wisconsin_Technical_College/College_Algebra_(NWTC)/06%3A_Conic_Sections/6.03%3A_EllipsesWe may imagine taking a length of string and anchoring it to two points on a piece of paper. The curve traced out by taking a pencil and moving it so the string is always taut is an ellipse.
