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

Skilled2021-02-14Added 84 answers

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.

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