The curves formed when a plane and a cone cross are known as conic sections or sections of a cone. A cone or conic section consists of three main sections: an ellipse, a hyperbola, and a parabola (the circle is a specific sort of ellipse). The conic parts are made from a cone with two identical nappes. Although the forms of the various portions of a cone or conic vary, they all have some similar characteristics, which we shall discuss in the sections that follow.

Well, in this reading, I’ll be exploring what Conic Section is, its Application, diagram, overview, & types.

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**What Is Conic Section?**

A **conic **section, conic or a quadratic curve is a curve obtained from a cone’s surface intersecting a plane. 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 Pergo’s systematic work on their properties.

The methodical study of conic sections’ characteristics by Apollonius of Pergo circa 200 BC marked the pinnacle of Greek mathematicians’ understanding of these sections. The degree of eccentricity determines the kind of conic. A conic in analytical geometry is a planar algebraic curve of degree 2, or the collection of points whose coordinates solve a matrix-form quadratic equation in two variables.

The geometric characteristics of conic sections may be deduced and expressed algebraically using this equation. The three varieties of conic sections have many characteristics in common, despite their apparent differences on the Euclidean plane. An extension of the Euclidean plane to a line at infinity yields a projective plane, which eliminates the apparent difference: a parabola’s two ends meet to form a closed curve tangent to the line at infinity, and a hyperbola’s branches meet in two points at infinity, forming a single closed curve.

A point, a line, or two intersecting lines will be formed when a plane passes through the cone’s vertex. Some writers do not even think of them as conics; instead, they refer to them as degenerate conics. In this article, “conic” will refer to a non-degenerate conic unless otherwise specified. Conics come in three different varieties: ellipse, parabola, and hyperbola. The circle is a unique variety of ellipse, even though Apollonius was originally thought to be a fourth sort. When the plane and cone connect in a closed curve, ellipses form.

Universal gravitation plays a crucial role in the construction of telescopes, such as the Herschel optical observatory in La Palma, Canary Islands. Conic sections are the orbits of two heavy objects that interact according to Newton’s law of universal gravitation, with their shared center of mass at rest. These sections follow parabolas or hyperbolas when traveling apart and ellipses when moving together.

Radio telescopes, optical telescopes, and searchlights are designed with the conic sections’ reflecting qualities in mind. A primary parabolic mirror in La Palma reflects light towards a secondary hyperbolic mirror, which reflects it back to a focus behind the first mirror. This arrangement is used by the Herschel optical telescope, demonstrating the importance of conic sections in astronomy.

**How Does Conic Section Works?**

A conic section is a type of geometric structure that can be defined in terms of plane geometry, with the locus of all points P being the distance between P and a fixed line L (referred to as the directrix). In the Euclidean plane, a circle is a limiting case that is not specified by a focus and directrix. The eccentricity of an ellipse is measured by how far it deviates from a circle, and its directrix is the line at infinity in the projective plane.

Conic parameters in an elliptical situation include eccentricity (e), foci, and directrix. The center of a conic section is the midway of the primary axis, which is the line connecting an ellipse’s or hyperbola’s foci. A circle is a special type of ellipse where the cutting plane is parallel to the base of the cone. The value of eccentricity(e) for a circle is e = 0. The general form of the equation in a circle with center at (h, k) and radius r: (x−h)2 + (y−k)2 = r2 is (x−h)2 + (y−k)2 = r2.

A parabola conic section results when the intersecting plane is at an angle to the cone’s surface. It is a line-symmetric curve with a similar form to the graph of y = x2, representing the graph of a quadratic function. This kind of curve is suitable for a projectile’s route when it is affected by gravity. Ellipse conic sections are formed when a plane intersects a cone at an angle, forming an ellipse with a main axis and a minor axis, or two foci. Eccentricity(e) for an ellipse has a value of e < 1. The equation for an ellipse’s conic section is (y-k)2/b2 + (x-h)2/a2 = 1.

Hyperbola conic sections are created when the fascinating plane intersects both nappes of the double cone and is parallel to the cone’s axis. The branches are the two disconnected halves of the hyperbola, with their arms being diagonally opposed and near the edge of a line.