I'm trying to construct a parametrization of the biggest ellipse whose y's $\in$ $(0,1]$ and whose x's $\in$ $[-1,1]$. I know that the equation of an ellipse of $x^2/a^2+y^2/b^2$=1. I've played around with the equation and haven't been able to make the biggest ellipse whose minimum x = -1, whose maximum x=1, i,e. domain $\in$ [-1,1] and whose codomain or y-values range from $\in$ (0,1] even in standard form so I don't know how I'll make the equation into parametric form.
Edit:
I'm actually not trying to find the biggest ellipse. I'm just trying to find some ellipse that must go through (-1,1) to (1,1)
$$x^2+\frac{(y-1)^2}{0.9^2} =1$$ has parametrization $$(x,y)=(\cos t, 1+0.9\sin t),$$ where $\pi\leq t\leq 2\pi$.