I am new about conic in projective geometry since it seems to be really different in euclidean plane.(adsbygoogle = window.adsbygoogle || []).push({});

A conic is a subset of P2 given by a homogenous quadratic equation:

aX^2 + bY^2 + cZ^2 + dXY + eXZ + fYZ = 0

why is it homogeneous?

meanwhile, it suitable coordinates we have aX^2 + bY^2 + cZ^2 = 0, with a, b, c element {0, 1, -1}.

why the part of dXY + eXZ + fYZ can be erased?

what is the difference of degenerate conic and non-degenerate conic?

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# Basic thing of Conic in Projective Geometry

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