exo7 5524

Construire les courbes de paramétrisations :

1

{x=t3(t+1)2(t−1)y=t2t2−1\left\{\begin{array}{l} x=\frac{t^3}{(t+1)^2(t-1)}\\ y=\frac{t^2}{t^2-1} \end{array}\right.

2

{x=(t+2)e1/ty=(t−2)e1/t\left\{\begin{array}{l} x=(t+2)e^{1/t}\\ y=(t-2)e^{1/t} \end{array}\right.

3

{x=(t−1)ln⁡(∣t∣)y=(t+1)ln⁡(∣t∣)\left\{\begin{array}{l} x=(t-1)\ln(|t|)\\ y=(t+1)\ln(|t|) \end{array}\right.

4

{x=2t1+t2y=t+21−t2\left\{\begin{array}{l} x=\frac{2t}{1+t^2}\\ y=\frac{t+2}{1-t^2} \end{array}\right.

5

{x=tt2−1y=t+2(t−1)2\left\{\begin{array}{l} x=\frac{t}{t^2-1}\\ y=\frac{t+2}{(t-1)^2} \end{array}\right.

6

{x=t3t2−9y=t(t−2)t−3\left\{\begin{array}{l} x=\frac{t^3}{t^2-9}\\ y=\frac{t(t-2)}{t-3} \end{array}\right.

7

{x=t31+3ty=3t21+3t\left\{\begin{array}{l} x=\frac{t^3}{1+3t}\\ y=\frac{3t^2}{1+3t} \end{array}\right.

8

{x=t2+t3y=t2+t3−2t4−2t5\left\{\begin{array}{l} x=t^2+t^3\\ y=t^2+t^3-2t^4-2t^5 \end{array}\right.

Exercice 4Fy0

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