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Conic Section

A conic section is a curve formed by the intersection of a plane and a cone. In mathematics, conic sections are classified into four types: ellipses, parabolas, hyperbolas, and degenerate conics.

Senses:

1. Mathematical Sense

In mathematics, a conic section refers to any of the four curves generated by intersecting a cone with a plane. These curves are:

1. Ellipse: A closed curve that resembles a squashed circle, where the sum of the distances from any point on the curve to two fixed points (foci) is constant.
2. Parabola: An open curve that is symmetric and has a focus and a directrix, where the distance from any point on the curve to the focus is equal to the perpendicular distance from that point to the directrix.
3. Hyperbola: A pair of open curves that are symmetric and have two foci, where the difference in distances from any point on each curve to the two foci is constant.
4. Degenerate Conics: Special cases where the conic section reduces to a point, a straight line, or two intersecting lines.

Example sentence: The shape of the planetary orbits can be described as conic sections, with each planet following an elliptical path around the sun.

2. Popular Sense

Outside of mathematics, the term "conic section" is not commonly used in everyday language.

Example sentence: During her vacation, Emily visited the popular tourist spot known for its conic section sculptures.

3. Local Sense

In certain localities, "conic section" may have a specific meaning or usage unique to that area.

Example sentence: In our local community, there is an annual conic section festival celebrating the beauty of mathematical curves.

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Explore books and resources related to conic sections on Amazon:

• Conic Sections: Mathematics
• Conic Section Sculpture