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C4 Parametric equation of curve

Hello all, hope you can help with the following question:

A curve is defined by the parametric equations x=t2+2t,y=t2−2tx=t^2 + \frac{2}{t}, y=t^2 - \frac{2}{t}.

Verify that the Cartesian equation of the curve is (x+y)(x−y)2=k(x+y)(x-y)^2=k, stating the value of the constant k.k.


I'm really stuck here, and feel like I'm missing something simple. The previous examples I've dealt with have been much easier. How do I express t in terms of x/y?

Thanks!
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BabyMaths
Original post by Dental Plan
Hello all, hope you can help with the following question:



I'm really stuck here, and feel like I'm missing something simple. The previous examples I've dealt with have been much easier. How do I express t in terms of x/y?

Thanks!



You don't need to.

x+y=2t2x+y=2t^2

(x−y)2=...(x-y)^2=...

(x+y)(x−y)2=...(x+y)(x-y)^2=...
Reply 2
Avatar for Dental Plan
Dental Plan
OP
Original post by BabyMaths
You don't need to.

x+y=2t2x+y=2t^2

(x−y)2=...(x-y)^2=...

(x+y)(x−y)2=...(x+y)(x-y)^2=...


Hah, thanks.

x+y=2t2x+y=2t^2

(x−y)2=16t2(x-y)^2=\frac{16}{t^2}

(x+y)(x−y)2=32t2t2=32(x+y)(x-y)^2=\frac{32t^2}{t^2}=32

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