Conic Section : - Ellipse and Parabola

Posted Date: 01 Nov 2009	Resource Type: Articles/Knowledge Sharing	Category: Education
Author: Sunil Saharan	Member Level: Diamond
Rating:	Points: 10 (Rs 5)

Hello Friend,
Conic section is the most important topic of mathematics that is useful in our general life as well. Now I am going to tell you about conic section. Introduction : -
Basically a conic section is a locus of a point say P which moves so that its distance from a fixed point is always in a constant ratio to its perpendicular distance from a fixed straight line.
Terms Used in Conic Sections : -

Focus : - The fixed point is called the focus of the conic section.
Directrix : - The fixed straight line is called the directrix.
Axis : - The straight line passing through the focus and perpendicular to the directrix is called axis.
Eccentricity : - The constant ratio between a and b is called the eccentricity. It varies with the type of conic section.
Latus Rectum : - The double ordinate passing through the focus and parallel to the directrix is known as latus rectum.

Ellipse : -
- Equation : - [x²/a²]+[y²/b²] = 1
- Major Axis = 2a
- Minor Axis = 2b
- Equation of directrix is x=+/- a/e
- eccentricity i.e. Is given by e² =1 - b²/a²
Parabola : -
- Equation : - y²=4ax
- Vertex is (0 , 0)
- Focus is (a , 0)
- Axis of the parabola is y = 0
- Directrix of the parabola is x+a=0
- Latus rectum =4a
- y²=-4ax
- x²=4ay
- x²=-4ay

I hope this will help you to solve your mathematics problems as well as will helpful in your general life.

-by,
Sunil Saharan

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