Question

# Whether the statement “I noticed that depending on the values for Aand 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” “makes sense” or “does not make sense”, And explain your reasoning.

Conic sections
Whether the statement “I noticed that depending on the values for Aand 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” “makes sense” or “does not make sense”, And explain your reasoning.
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.