Conic Sections And Equations Of The Second Degree

posted on: 22 Aug, 2012 | updated on: 28 Aug, 2012

Conic section can be defined as a curve that is obtained by Intersection (Cartesian product) of a cone with a plane. In analytic Geometry conic section can be defined as an algebraic curve that has degree 2. Here we will discuss conic sections and equations of the second degree. General equation of any conic section is given as:
Fp² + Gpq + Hq² + Ip + Jq + K = 0;
If value of F = 0 then we will get ‘F’ and ‘H’ in the equations. Different types of conic sections are Parabola, Circle, Ellipse and Hyperbola. Here we will discuss each conic section with help of a table mentioned below:

Name of conic section	Relationship of F and H
Parabola	F = 0 or H = 0 but both values of ‘F’ and ‘H’ will never be equals to 0.
Circle	In case of Circle value of ‘F’ and ‘H’ are equal.
Ellipse	In case of ellipse sign of ‘F’ and ‘H’ are same but ‘F’ and ‘H’ are not equal.
Hyperbola	In case of hyperbola signs of ‘F’ and ‘H’ are opposite.

Let’s see which equations are taken in second degree equation. In mathematics, generally we consider polynomial and quadratic equations in second degree equation. For example: Suppose we have an equation ax² + bx + c = 0. Given equation is said to be Quadratic Equation because it has highest degree of 2 (square). To solve second order quadratic equation formula is defined which is given as:
X = -b + √ b² – 4ac / 2a.
Circle, Parabola, Ellipse, hyperbola equation also has order of degree 2.
This is all about Conic sections and equations of the second degree.

Topics Covered in Conic Sections And Equations Of The Second Degree

Equations in Polar Coordinates

posted on: 22 Aug, 2012 | updated on: 23 Aug, 2012

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Transformation to Rectangular Coordinates

posted on: 22 Aug, 2012 | updated on: 23 Aug, 2012

A Point in mathematics can be represented using two representations namely rectangular or Cartesian and polar coordinate form. Later one is described in terms of angle that specifies the direction of vector and a particular distance from a fixed point representing the magnitude of vector. Let there be a point whose polar form is given as:
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Simplification of the Equation in Rectangular Coordinates

posted on: 22 Aug, 2012 | updated on: 23 Aug, 2012

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