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Conic section

Adapted from Wikipedia · Explorer experience

Diagram showing the four types of conic sections: circle, ellipse, parabola, and hyperbola.

Conic Section

A conic section is a special shape you get when a flat surface cuts through a cone. Imagine a ice cream cone, and then imagine a knife slicing through it. Depending on how you slice it, you can get different shapes!

There are three main types of conic sections: the ellipse, the parabola, and the hyperbola. A circle is a special kind of ellipse.

Long ago, around 200 BC, ancient Greek mathematicians started studying these shapes. A smart mathematician named Apollonius of Perga did a lot of important work on them.

Conic sections can also be described using a special point called a focus and a line called a directrix. The shape you get depends on how far points of the curve are from this focus and this line.

These shapes are not just fun to look at—they are used in many areas of science and engineering. For example, the paths of planets and stars are conic sections. Special mirrors used in searchlights and telescopes also use the shape of a parabola.

Conic sections have been studied for thousands of years and are an important part of Euclidean geometry. They help us understand many things in nature and technology!

Images

A helpful diagram showing how different angles of cutting planes create the three types of conic sections.
Diagram showing different types of conic sections based on eccentricity
Diagram showing the standard shapes of parabolas, a type of conic section in geometry.
An old scientific drawing showing different types of conic sections, like circles and ellipses, from an 18th-century book.
Diagram showing the different standard shapes of an ellipse in geometry.
Diagram showing the standard forms of a hyperbola, a type of conic section.
Animation showing how shapes change from a circle to an ellipse, parabola, and hyperbola by adjusting their eccentricity.
An ancient geometric diagram showing conic sections, helping us understand the shapes described by Greek mathematician Apollonius of Perga.
Animation showing how to draw an ellipse using the parallelogram method—a geometry technique used in engineering and math.

Related articles

Ellipse
Parabola
Circle
Apollonius of Perga
Curve
Euclidean geometry

This article is a child-friendly adaptation of the Wikipedia article on Conic section, available under CC BY-SA 4.0.

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