Conic Sections:

Conic Sections:

In mathematics, a conic section (or just conic) is a curve obtained by intersecting 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. It can be defined as the locus of points whose distances are in a fixed ratio to some point, called the focus, and some line, called the directrix.Algebra is the one of the most important chapter in mathematics subject. Here the Conic section is one of the topics in algebra chapter. In mathematics a conic section (or just conic) is a curve obtained by intersecting 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. The conic sections were named and studied as long ago as 200 BC.
Let us now learn the definition of a Conic Section:
Conic section is generally defined as intersection of a plane and a cone, it will depend on How the plane is oriented, the curve will be one conic sections. Or a conic section is a curve formed by the intersection of a cone with a plane.

Four types of conic sections are there,

* Circle,
* Parabola,
* Ellipse, and
* Hyperbola.

Explanation:

* A circle is the set of all points; having the area is equal distance from a fixed point C, the midpoint (center) of the circle.
* An ellipse is the set of all points; and it is surrounded two foci, (or) focus points, such that the sum of the distances from any point to each focus remains constant. An ellipse can be oriented vertically or horizontally.
* A parabola is the set of points; and that are equal distance from the focus point and the directrix, a fixed line. A parabola can be oriented vertically or horizontally.
* A hyperbola is the set of all points; it’s around two foci, or focus points, such that the difference of the distance from any point to each focus all remains constant. A hyperbola can be oriented vertically or horizontally

General Equation for a Conic Section:

General equation for conic section: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0.
The conic sections could involve these all:

1. The description of cones apart from the coordinates
2. The description of cones with coordinates, so that this is through equation or formulas for them.
3. The choice from the orthogonal coordinate system is (x, y, z) such that the plane, so it is corresponding to Z = 0, and a description of the cone with in coordinate system.
4. The transformation of quadratic equation is standard form by a combination of rotation.
5. Using the equation in standard form to classify the intersection as an ellipse, parabola, hyperbola etc...
6. And It has the equation of Ax2 + Bxy + Cy2 + Dx + Ey + F = 0.

Hope you like the above example of Conic Sections.Please leave your comments, if you have any doubts.