Curve sketching (1 Viewer)

[Petyo]

Does anyone know the complete proof for a curve to form a loop, for example if you are to prove that this curve:x=t^2 and y=t(4-t^2) forms a loop???
THanks in advance, guys

 

[MC Squidge]

sketch the curve i guess

 

[kaz1]

You could look for two y values for one x value.

 

[shaon0]

Does anyone know the complete proof for a curve to form a loop, for example if you are to prove that this curve:x=t^2 and y=t(4-t^2) forms a loop???
THanks in advance, guys

y=+-sqrt(x)(1-x)
Check the derivative at pts: x=0, and 1 and/or look for critical pts ie. Where the derivative is equal to undefined.

 

[MaNiElla]

 

[tehrobzorz]

what do you mean by looop? like a circle?

 

[LordPc]

you could always find t in terms of x/y and then substitute into y/x to get a cartesian equation which you would be more familiar with.

in this case you should get t = x^1/2. so subbing into y you should get sqrt x's and therefore the graph only exists to the right of the y axis. and graph from there. also note that if doing this would clearly give you the equation of a circle

 

[Iruka]

You need to show that the curve passes through the same point for two different values of the parameter.

In this case, if t=2, you get x=4, y=0. And if t=-2, you get x=4 and y=0, again.

You would also need to show that both x(t) and y(t) are continuous functions of t in between these two values, I guess. (Which they clearly are in this case).