I have been taught that the equation [tex] Ax^2 + Cy^2 +Dx + Ey +F = 0 [/tex] represents a general form of conics.(adsbygoogle = window.adsbygoogle || []).push({});

Then the conditions of the coefficients in the equation could identify which type of conics the equation represents...

Circle: A=C

Ellipse: A does not=C and AC>0

Hyperbola: AC<0 and if the coefficients have opposite signs

Parabola: A=0 OR C=0

The thing that I do not understand is why... I was wondering if anyone knows a way to explain the reasons to me?

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# Homework Help: Conditions on the coefficients of conics equations

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