Question 979290
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Collect like terms in the LHS.  That is, put the equation in General Form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ Ax^2\ +\ Bxy\ +\ Cy^2\ +\ Dx\ +\ Ey\ +\ F\ =\ 0]


If *[tex \LARGE A\ =\ B\ =\ C\ =\ 0] then you don't have a conic.


IF *[tex \LARGE A\ =\ C], circle


If *[tex \LARGE A\ \not =\ C] and *[tex \LARGE AC\ >\ 0], ellipse


If *[tex \LARGE A\ \not =\ C] and (*[tex \LARGE A\ =\ 0] or *[tex \LARGE C\ =\ 0]), parabola


if *[tex \LARGE AC\ <\ 0] or *[tex \LARGE A\ =\ C\ =\ 0], hyperbola


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \