Emeli Hagan

2021-02-13

Whether the statement “I noticed that depending on the values for Aand B assuming that they are not both zero, the graph of $A{x}^{2}+B{y}^{2}=C$ can represent any of the conic sections other than a parabola” “makes sense” or “does not make sense”, And explain your reasoning.

Viktor Wiley

Consider the equation, $A{x}^{2}+B{y}^{2}=C$ 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 $A{x}^{2}+B{y}^{2}=C$ 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 $A{x}^{2}+B{y}^{2}=C$. 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 $A{x}^{2}+B{y}^{2}=C$ Hence the statement “I noticed that depending on the values for A and B assuming that they are not both zero, the graph of $A{x}^{2}+B{y}^{2}=C$ 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.