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 Why this equation, x²+y²+2ax+2by+c=0, is called 'normal form of the conic section equation'.
Hi,
The following is called normal form of the conic section equation:
x²+y²+2ax+2by+c=0
A circle is one of the conic sections when considered as a special of ellipse. I'm confused as to why the the given equation is called "normal form of the conic section equation" when, in my opinion, the equation only describes a circle, a point which could be said to be a special case of circle, imaginary locus or imaginary circle; as I understand it the equation has nothing to do with the conic sections other than the circle which is a special case. Could it represent any other conic section?
The shown below is equation in its context:
I have tried below to relate the "normal form of the conic section equation" to general equation of a circle with radius R and center at (x₀, y₀).
Thank you for your help and time!
The following is called normal form of the conic section equation:
x²+y²+2ax+2by+c=0
A circle is one of the conic sections when considered as a special of ellipse. I'm confused as to why the the given equation is called "normal form of the conic section equation" when, in my opinion, the equation only describes a circle, a point which could be said to be a special case of circle, imaginary locus or imaginary circle; as I understand it the equation has nothing to do with the conic sections other than the circle which is a special case. Could it represent any other conic section?
The shown below is equation in its context:
I have tried below to relate the "normal form of the conic section equation" to general equation of a circle with radius R and center at (x₀, y₀).
Thank you for your help and time!
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