Consider the equation,
\(Ax^2 + By^2 = C\)
When A and B both appear are on the same side and have
coefficients with opposite sign, the equation is that of a hyperbola.
So the equation of hyperbola is \(Ax^2 + By^2 = C\)
When A and B both appear are on the same side and have
coefficients with same sign, the equation is that of an ellipse. So the
equation of ellipse is \(Ax^2 + By^2 = C\).
When A and B terms both appear are on the same side and are
equal, the equation is that of a circle. So the equation of circle is
\(Ax^2 + By^2 = C\)
Hence the statement “I noticed that depending on the values for A
and B assuming that they are not both zero, the graph of
\(Ax^2 + By^2 = C\) can represent any of the conic sections other than a
parabola.” Make sense.
Conclusion:
The equation of parabola must have either \(x^2 or y^2\) term.