Foremost, you will have to know that when you talk about Conic Sections, it merely means that a Section is obtained from a CONE, by using a plane to Cut|Chop|Intersect|Bisect, name it what you want.
The Cone that we use here is a Right Circular Cone, and its general Equation is given as follows.
What is the General Equation of a Conic Section ?

Conditions required to obtain various CONIC figures

What is a Conic section ?

Can you tell us the shapes|Curves, produced from a Conic section ?

How is the Circle formed from a Cone ?

How is an Ellipse formed ?

How is a Parabola formed ?

How is a Hyperbola formed ?

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