How do I tell the difference between a non conic function and a conic function by looking at an equation?
If your function contains terms of the type ax^2, ay^2, ax, and ay along with some constant terms , and where a is a rational number, then you have a conic
if it contains terms such as xy , it could be a conic that has been rotated, and is no longer parallel or perpendicular to the axes
We call then conics because they are a result of slicing a cone and looking at the resultiong surface.
Visualize a cone sitting on a table in front of you.
If you slice it with a cut parallel to the table, looking at your slice you see a circle
if you slice it with a slant, but the cut does not reach the base of the cone, you will see an ellipse.
if you slice it with a slant so that it also cuts the base, you will see a parabola.
if your slice it perpendicular to the base, the slice will look like a hyperbola.
You might want to Google "conic sections" to see images of that