# Conic Sections And Equations Of The Second Degree

Conic section can be defined as a curve that is obtained by Intersection (Cartesian product) of a cone with a planeIn 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.

## Equations in Polar Coordinates

Polar coordinate is a coordinate system in which each Point on coordinate plane is calculated using distance from a fixed point and an angle from fixed direction.

In Polar Coordinate Plane fix point is called pole and line segment from the pole in fixed direction is called as polar axis. Distance that is measured from pole is called as radial distance a...Read More

## Transformation to Rectangular Coordinates

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:
Q (n ...Read More

## Simplification of the Equation in Rectangular Coordinates

Simplification of the equation in rectangular coordinates is similar to solving two Linear Equations with two unknown variables. Rectangular coordinates are nothing but the points that lie on the line whose equation in general is written for all such points. In fact general equation of line is given in the form of rectangular coo...Read More

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