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Defining conic sections a conic section or simply conic is a curve obtained as the intersection of the surface of a cone with a plane.
How to identify the conic section. For example take a look at 3 x 2 12 x. How to identify the four conic sections in equation form. Standard forms of equations of conic sections.
Distance between center and either focus is c with. It looks like a u curve. A 3x2 3y2 6x 9y 14 0 b 6x2 12x y 15 0 c x2 2y2 4x 2y 27 0.
Classify the following equations according to the type of conic each represents. The circle is type of ellipse and is sometimes considered to be a fourth type of conic section. Classifying conic sections another way to classify a conic section when it is in the general form is to use the discriminant like from the quadratic formula.
A single focus a fixed line called the directrix and the ratio of the distances of each to a point on the graph. We get circles when we cut our cone straight across. In the picture above the number one cone is the parabola.
When a conic is written in the form ax 2 by 2 cx dy e 0 then the following rules can be used to determine what type of relation it is. The shapes that you get from slicing a cone are called conic sections. Now picture another one directly underneath it that is.
Distance between center and either focus is c with. The equations y x 2 4 and x 2 y 2 3. The three types of conic sections are the hyperbola the parabola and the ellipse.
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