Solve Lissajou's Figure Problem with 1:2 Frequency Ratio

[Amith2006]

Homework Statement

The problem in which I have difficulty has been posted as an attachment. It is based on Lissajou's figure. In the given problem, the ratio of the frequency is 1:2 but nothing has been mentioned about the phase difference. As far as my knowledge goes, the corresponding Lissajou's figure can either be a parabola or a figure of eight. The difficulty that I am facing is that, both the options are given. Is there any additional information that I have failed to notice in the question? Any help is most welcome.

Homework Equations

The Attempt at a Solution

 

[berkeman]

Homework Statement

The problem in which I have difficulty has been posted as an attachment. It is based on Lissajou's figure. In the given problem, the ratio of the frequency is 1:2 but nothing has been mentioned about the phase difference. As far as my knowledge goes, the corresponding Lissajou's figure can either be a parabola or a figure of eight. The difficulty that I am facing is that, both the options are given. Is there any additional information that I have failed to notice in the question? Any help is most welcome.

Homework Equations

The Attempt at a Solution

If it were a figure 8, which way would the figure 8 be oriented?

 

[willem2]

As I read the question, three could be more than 1 correct option, but take good look
at that figure 8.

 

[Amith2006]

Do u mean that the figure 8 should have been aligned in the horizontal plane? Hence the more appropriate answer is the parabola. Am I heading in the right direction now?

 

[berkeman]

Do u mean that the figure 8 should have been aligned in the horizontal plane? Hence the more appropriate answer is the parabola. Am I heading in the right direction now?

It's not a parabola, but about the figure 8, yes.