What are the Conic Sections?


A conic or conic section is a curve formed by bisecting a right circular conical surface with a plane. The conic sections are observed in the path used by the astronomical materials. According to Newton’s law of universal gravitation, when two massive objects interact, their orbits are conic sections. In this case, their common centre of mass is estimated to be at rest. The study of conic sections is not only important to Physics, Astronomy, and Mathematics but also applied in a variety of engineering applications. An important property called smoothness of conic sections is mainly used in aerodynamics, where it ensures the laminar flow and prevents disturbance.

When a plane is parallel to the side of a cone, then the resulting curve is a parabola.  It is a plane curve and is approximately U-shaped. It involves focus (point), directrix (focus). It is defined as a locus of points in the plane that are equidistant from both the focus and directrix. Its eccentricity is 1. The equation in different orientations are:

When F = (a,0), then y2 = 4ax

When F = (-a, 0), then y2 = – 4ax

When F = (0, a), then x2 = 4ay

When F = (0, -a),  then x2 = – 4ay

When a plane is slightly tilted over a cone, then the curved obtained is an ellipse. An ellipse is a closed type of conic section. It is defined as a set of points on a plane in which the distance from the two fixed points is constant. It usually looks like a squashed circle. It has many similarities with the other two forms of conic sections. It is also considered as an angled cross-section of a cylinder. Its eccentricity is less than 1 but greater than 0. The standard equation of the ellipse centred at the origin with width 2a and the height 2b is given by

(x2/a2) + (y2/b2) =1

When the plane cuts both the extensions of a cone, then the resulting curve is called a hyperbola. It has two curves that are the mirror images of each other. It means that they are open in opposing sides. Its eccentricity is greater than 1. The standard equation in a coordinate plane is given by

(x2/a2) – (y2/b2) =1

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