Conic Section

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Conic Section is generally formed by the intersection of double cone and plane. It generally relates with

ellipse, circle, hyperbola and parabola with different equations. Hyperbola and Parabola have two different

equations depending upon its axis.

General form of the conic section is represented by the following equation:-

(Ax)^2 + (B x y) + (C y) ^2 + (Dx) + (E y) + F = 0

This concept can be more clarified by the examples. Two related examples are shown below for the

understanding purpose of conic section.


Example 1: An ice-cream cone is cut into a section. The eccentricity of this conic section is 1.5.

What will be the conic section?



Solution: Eccentricity is the measure of how much the conical section varies from being circular. The value

of eccentricity helps to decide what type of curve the conic section is. Eccentricity shows how un-circular the

curve is. Higher the eccentricity, lesser the curvature. In the given problem eccentricity is 1.5 therefore it is a

hyperbola.

 
Example 2: What is the length of the Latus rectum of an ellipse equal to?

Solution: The latus rectum is a line that is parallel to the directrix and passes through the focus. The lengths

of different conic sections are different. Like for parabola the length of latus rectum is 4 times the focal

length. In the given problem the conic section is ellipse therefore the length of latus rectum is 2b^2/a, where a

and b are half of major and minor diameter.



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