Algebra Conic Sections

Introduction:

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.

(Source from wiki pedia)

Conic Sections:

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: 

The description of cones apart from the coordinates
The description of cones with coordinates, so that this is through equation or formulas for them.
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.
The transformation of quadratic equation is standard form by a combination of rotation.
Using the equation in standard form to classify the intersection as an ellipse, parabola, hyperbola etc...
And It has the equation of Ax2 + Bxy + Cy2 + Dx + Ey + F = 0.

Algebra is widely used in day to day activities watch out for my forthcoming posts on math help for algebra 2 and free algebra 2 answers. I am sure they will be helpful.

Example:

Equation of parabola:

A parabola is the group (set) of points, which are equal distance from the both fixed point and fixed line. Parabolas are generally U-shaped, it having two arms, that is extended to infinity.

Y2 = 4aX