Parabolas, Ellipses and Hyperbolas
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Definition of a parabola:
A parabola is a set of all points in a plane that are equidistant from a given fixed point (the Focus) and a given straight line (the Directrix).
Different cases of parabolas:
 With the vertex at the origin, the parabola opens in the positive x direction and has the equation where vertex=(0,0) and focus is the point (p,0).
 With the vertex at the origin, the parabola opens in the negative x direction and has the equation where vertex=(0,0) and focus is the point (p,0).
 With the vertex at the origin, the parabola opens in the positive y direction and has the equation where vertex=(0,0) and focus is the point (0,p).
 With the vertex at the origin, the parabola opens in the negative y direction and has the equation where vertex=(0,0) and focus is the point (0,p).
Definition of an ellipse:
An ellipse is a set of all points in a plane, whose distances from two fixed points (the foci) is a positive constant.
Different cases of ellipses:
 The vertex is at the origin and the foci and the major axis are on the xaxis with the center at the origin and has the equation of the form where the foci and the major axis are on the xaxis, the length of the major axis is 2a, the minor axis is on the yaxis, the length of minor axis equals to 2b and the center of the origin is at the origin (0,0).
 The vertex is at the origin and the foci and the major axis are on the yaxis with the center at the origin and has the equation of the form where the foci and the major axis are on the yaxis, the length of the major axis=2a, the minor axis is on the xaxis, length of the minor axis=2b and the center is at the origin (0,0).
Definition of a hyperbola:
A hyperbola is a set of all points in a plane, the difference of whose distances from two fixed points (the foci) is a positive constant.
Different cases of hyperbolas:
 The center is at the origin and the foci are on the xaxis and conjugate axis is the yaxis and has the equation of the form where the foci and the vertices are on the xaxis, the distance between the foci=2a, the conjugate axis is on the yaxis and the center is at the origin (0,0).
 The center is at the origin and the foci are on the yaxis and conjugate axis is the xaxis and has the equation of the form where the foci and the vertices are on the yaxis, the distance between the foci=2a, the conjugate axis is on the xaxis and the center is at the origin.
Asymptotic Equations:
The equations of the asymptotes to the hyperbola are as follows and .

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"Title" Tutorial Summary : 
This tutorial introduces the conic sections and their different features. A general discussion of the brief history of conic sections and the formation of them is shown with graphical illustrations. Key conic sections such as a parabola and their properties are shown in the examples.
Ellipses and hyperbolas are defined with the help of graphs and the examples in this tutorial. Different scenarios where ellipses, hyperbolas change direction as far as their graphs are discussed in the sections of the tutorial. The foci and vertices of hyperbolas and ellipses are essential to the development of their graphs.

Tutorial Features: 
Specific Tutorial Features:
• Step by step examples of the different aspects of the conic sections.
• “Completion of square” trick is used to bring the equations of the conic sections in standard form.
Series Features:
• Concept map showing interconnections of new concepts in this tutorial and those previously introduced.
• Definition slides introduce terms as they are needed.
• Visual representation of concepts
• Animated examples—worked out step by step
• A concise summary is given at the conclusion of the tutorial.

"Title" Topic List: 
Introduction to Conic Sections A Brief History of the Conic Sections Some applications Parabola Definition of a parabola Different types of equations of a parabola Ellipse Definition of an ellipse Relationship between foci and axes Different types of equations of an ellipse Hyperbola Definition of a hyperbola Relationship between foci and vertices Mechanical vs. electromagnetic waves Different types of equations of a hyperbola Asymptotes of a hyperbola 
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