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
ANSWERED
asked 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 \(Ax^2 + By^2 = C\) can represent any of the conic sections other than a parabola” “makes sense” or “does not make sense”, And explain your reasoning.

Answers (1)

2021-02-14
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.
0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

asked 2020-10-21
Determine whether the statement, 'I noticed that depending on the values for A and C, assuming that they are not both zero, the graph of \(\displaystyle{A}{x}^{{{2}}}+{C}{y}^{{{2}}}+{D}{x}+{E}{y}+{F}={0}\) can represent any of the conic sections', makes sense or does not make sense, and explain your reasoning.
asked 2021-05-22
Sheila is in Ms. Cai's class . She noticed that the graph of the perimeter for the "dented square" in problem 3-61 was a line . "I wonder what the graph of its area looks like ," she said to her teammates .
a. Write an equation for the area of the "dented square" if xx represents the length of the large square and yy represents the area of the square.
b. On graph paper , graph the rule you found for the area in part (a). Why does a 1st−quadrant graph make sense for this situation? Are there other values of xx that cannot work in this situation? Be sure to include an indication of this on your graph, as necessary.
c. Explain to Sheila what the graph of the area looks like.
d. Use the graph to approximate xx when the area of the shape is 20 square units.
asked 2021-03-12

When using the half-angle formulas for trigonometric functions of \(\displaystyle\frac{\alpha}{{2}}\), I determine the sign based on the quadrant in which \(\alpha\) lies.Determine whether the statement makes sense or does not make sense, and explain your reasoning.

asked 2021-06-07
Determine whether each statement makes sense or does not make sense, and explain your reasoning. By modeling attitudes of college freshmen from 1969 through 2010, I can make precise predictions about the attitudes of the freshman class of 2020.
...