I see that you got it. I'll answer it anyway, for the sake of completeness.Originally Posted by pidgezero_one
The general form for an ellipse is:
where the center of the ellipse (the geometric center, not one of the foci) is at the coordinates (h,k).
Since we know the center is at (0,0) we know that h = k = 0 and the ellipse equation is:
Now, we have two points on the ellipse: (2,-2) and (-2/3,10/3). Putting these points into the ellipse equation gives us (respectively)
So we have two equations for a and b. This should suffice to solve the system. Equation 1 gives us:
Putting this into equation 2 gives us:
Since a is the length of the semi-major or semi-minor axis, we choose the positive value.
This gives a value for b as: .
Thus the equation for the ellipse is: