"Whether the statement “I noticed that depending on..." solved and explained

Emeli Hagan

Answered question

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.

Answer & Explanation

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} o r y^{2}

term.

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