Determining the nature of a curve

[Dumbass]

Greetings.

They give a curve whose parametric equations are:

They ask to determine if the curve is:
A straight line, a parabola, a circle, an ellipse, or a hyrperbola.

Here is what i did:


I am not about this one. Is this the right answer?

Thank you !

 

[JeffM]

Looks good to me.

 

[Steven G]

You work is correct.
I am not sure that I would have expanded out and collected like terms for two reasons--
1) You might have made a silly error and lose points on an exam.
2) It already is clear that you have an equation of a parabola even before expanding out and collecting like terms.

 

[Dumbass]

Looks good to me.

Thank you!

You work is correct.
I am not sure that I would have expanded out and collected like terms for two reasons--
1) You might have made a silly error and lose points on an exam.
2) It already is clear that you have an equation of a parabola even before expanding out and collecting like terms.

Thank you!