Leaf of Descartes

Someone,I need help in this.I have the answer but I can't think of a solution.I have tried a few things,though...

Parameterization of the leaf of Descartes.
y=tx => x= (3at)/(1+t^3)
y= (3at^2)/(1+t^3) (-infinity
And here are some things I have figured out,
When t<-1,
t+1<0, 1+t^3<0 and hence x>0

When 0>t>-1,
t+1>0, 1+t^3>0 and hence x<0

*Here are the hints my teacher gave me:
limx(t-->-1)= +/- infinity
limx(t-->-1,t<-1)=infinity
limx(t-->-1,t>-1)= -infinity

and here is the answer:
[โ€‹IMG]

Replies

  • PraveenKumar Purushothaman
    PraveenKumar Purushothaman
    Answer?
  • Aruwin
    Aruwin
    Praveen-Kumar
    Answer?
    Yes,the graph and the table are the answer but i dunno the solution.
  • simplycoder
    simplycoder
    Refer this, you would get the correct way atleast.
    Folium Of Descartes
  • Aruwin
    Aruwin
    simplycoder
    Refer this, you would get the correct way atleast.
    Folium Of Descartes
    Sorry,I have read through it and I have got the idea.But how come the graph that my teacher drew is different than that that is shown on wikipedia?
  • Aruwin
    Aruwin
    I am stucked now.
    I have tried to differentiate dy/dx=(dy/dx)/(dx/dt) and I got [2t(1+t^3) - 3t^4]/(1-2t^3) but I am not sure if this is right or not.
    So after I have differentiate this,what do I do next to make the graph table?
  • Aruwin
    Aruwin
    Hey guys,it is alright.I have solved it myself ๐Ÿ˜€ I searched on the internet about descartes folium and studied it and then i got it ๐Ÿ˜€
  • PraveenKumar Purushothaman
    PraveenKumar Purushothaman
    Aruwin
    Hey guys,it is alright.I have solved it myself ๐Ÿ˜€ I searched on the internet about descartes folium and studied it and then i got it ๐Ÿ˜€
    Thats great... ๐Ÿ˜€
  • Dancer_Engineer
    Dancer_Engineer
    Great! ๐Ÿ˜€

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