Answer:
[tex]\left\{\begin{matrix} x(t)=8cos(t) \\ y(t)= 6sin(t)\end{matrix}\right.[/tex]
Step-by-step explanation:
1) Firstly, the basic relations when it comes to parametrization:
[tex]\left\{\begin{matrix}x=acos(t) & \\ y=bsin(t) & \end{matrix}\right.\\[/tex]
2) The given ellipse:
[tex]\frac{x^{2}}{8}+\frac{y^{2}}{6}=1\\[/tex]
3) Let's parametrize it:
[tex]\frac{(x-p)^{2}}{a^{2}}+\frac{(y-q)^{2}}{b^{2}}=1\\[/tex]
a, b for the radii, and p, and q since it is centered at the origin then p and q i equal to zero. a = [tex]a=\sqrt{8} , b=\sqrt{6}[/tex]
Then parametrized:
[tex]\left\{\begin{matrix} x(t)=8cos(t) \\ y(t)= 6sin(t)\end{matrix}\right.[/tex]
Lastly, on the right the parametric curve where (8,0) t=0
