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# Parametric to Cartesian watch

1. A curve is defined by the parametric equation; x= t^3 / (t^2 +1) , y= t^2 / (t^2 +1) .

Show that the cartesian equation for the curve is y^3=x^2(1-y).

If someone could show me how to get this Cartesian equation, I will really appreciate it. Thanks
2. by inspection you can see that

x = yt

so

y = x/t

y3 = {x/t}3

y3 = {x3}
/{t3}

y3 = {x2}*x/ /{t3}

see if you can continue...
3. (Original post by the bear)
by inspection you can see that

x = yt

so

y = x/t

y3 = {x/t}3

y3 = {x3}
/{t3}

y3 = {x2}*x/ /{t3}

see if you can continue...

Thank you, I have tried this but I cannot get x/t^3 into (1-y). Could you please show me?
4. (Original post by AjayTaak)
Thank you, I have tried this but I cannot get x/t^3 into (1-y). Could you please show me?
i would start things off by rewriting :

(You could do this using other division methods)

That should help you see where comes from in the solution.
5. (Original post by AjayTaak)
Thank you, I have tried this but I cannot get x/t^3 into (1-y). Could you please show me?
x/t3 can be written as...

{ t3/{ 1 + t2 } }/t3...

====> 1/{t2 + 1 }

we need to show that

1 - y = 1/{t2 + 1 }

if you put in t2/{ 1 + t2 } for y the result emerges as required...

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