The eccentricity of any kind of curved shape will be characterising its shape regardless of the entire size of the whole thing. There are different types of things that will be getting formed whenever the plane will be intersecting the cone for example Circle, ellipse, parabola and hyperbola. These kinds of features will be perfectly characterised depending upon their shapes that will further be determining the concept known as eccentricity. The circle will be having zero eccentricity and the parabola will be having unit eccentricity. The ellipse and hyperbola will always be having varying eccentricities.

Concept of Eccentricity

 The comprehensive concept of the eccentricity of the conic section can be defined as the ratio of the distance from any point on the conic section to the focus of the perpendicular distance from that point to the nearest directrix. For any kind of conic section, the eccentricity of the conic section will be the distance of any point on the curve to its focus/the distance of the same point to the directrix is equal to a constant.

This particular constant value will be known as an eccentricity that can be perfectly denoted by alphabet it. The eccentricity of the curved shape will always help in determining how long that particular shape is and how to deal with the coming aspect very easily.

Following are some of the very basic inclusions which the people need to be clear about in this particular area:

  • Eccentricity zero means it will be there in the case of a circle
  • The eccentricity of the ellipse will be between zero and one
  • Eccentricity of parabola will always be equal to 1
  • The eccentricity of hyperbola will always be more than one and the eccentricity of the line will always be infinity.

Whenever the ellipse or hyperbola will have to focus into directrix the parabola will be one focus and one directrix. The eccentricity formula will be given in the cases of both of them and explain is:

 Eccentricity is equal to distance to the focus/distance to be directrix

  • Eccentricity is equal to C/A

 Hence, being clear about the implementation of this particular formula is very much important but on the other hand in the cases of the ellipse the formula will be eccentricity is equal to enter the root A square minus B square.

  • In the case A is greater than be then the formula will be eccentricity is equal to a square minus B square into the root/A

 In the above-mentioned formulas, A will be the semimajor axis, B will be any minor axis and C will be the distance from the centre to the ellipse or focus.

Hence, the following are some of the very basic tips which the kids need to follow in this particular area so that they can have a good command of the whole chapter very easily:

  • The eccentricity of the conic section will help in determining its curvature in the whole process
  • Eccentricity of the circle will be zero in parabola will be one
  • The different efficiencies of the ellipse in parabola will be calculated with the help of all the above-mentioned formulas so that kids can have a good command of the whole chapter very easily and there is no query in the minds of kids.

Apart from all the above-mentioned points being clear about the basic properties of the ellipse is another very important thing to be taken into consideration by the people and further, depending upon platforms like Cuemath is the best decision which the people can make in this particular area. This is considered to be the best way of ensuring that everybody will be on the right track of learning things so that overall goals are easily achieved and everyone can score well in exams.

By Punit