Conic Section

AN INTRODUCTION TO CONIC SECTIONS There exists a certain group of curves called Conic Sections that are conceptually kin in several astonishing ways. Each member of this group has a certain shape, and can be classified appropriately: as either a circle, an ellipse, a parabola, or a hyperbola. The term "Conic Section" can be applied to any one of these curves, and the study of one curve is not essential to the study of another. However, their correlation to each other is one of the more intriguing coincidences of mathematics. A CONIC SECTION DEFINITION Put simply, a conic section is a shape generated when a cone intersects with a plane. There are four main types of conic sections: parabola, hyperbola, circle, and ellipse. The circle is sometimes categorized as a type of ellipse. In mathematics, a conic section (or just conic) is a curve obtained as the intersection of a cone (more precisely, a right circular conical surface) with a plane. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2. There are a number of other geometric definitions possible. One of the most useful, in that it involves only the plane, is that a conic consists of those points whose distances to some point, called a focus, and some line, called a directrix, are in a fixed ratio, called the eccentricity. Traditionally, the three types of conic section are the hyperbola, the parabola, and the ellipse. The circle is a special case of the ellipse, and is of sufficient interest in its own right that it is sometimes called the fourth type of conic section. The type of a conic corresponds to its eccentricity, those with eccentricity less than 1 being ellipses, those with eccentricity equal to 1 being parabolas, and those with eccentricity greater than 1 being hyperbolas. In the focus-directrix definition of a conic the circle is a limiting case with eccentricity 0. In modern geometry certain degenerate cases, such as the union of two lines, are included as