"Give a pair of parametric equations for the ellipse:"



(x+3)^2/9 + (y-1)^2/6 =1

What does parametric mean and how do you find it?

The parametric equations of an ellipse are x=a\cdot{cos(t)}; \;\ y=b\cdot{sin(t)}

You have an ellipse centered at (-3,1) with major axis length 3 and minor axis length sqrt(6).

You have a=3; \;\ b=\sqrt{6}

\frac{x}{a}=cos(t), \;\ \frac{y}{b}=sin(t)

\frac{x+3}{3}=cos(t), \;\ \frac{y-1}{\sqrt{6}}=sin(t)

You have:

x=3cos(t)-3, \;\ y=\sqrt{6}sin(t)+1

Here is a graph of your ellipse.

I would suggest googling parametric equations, asking your instructor, getting a good book. It's too involved for me to address here, but I hope this helped.