Step $6$

We have determined that there are two points on the given ellipse that are the farthest possible distance away from the point $(-1,0).$ Both points have the $x-$coerdinate $x=\frac{1}{2},$ One point has the $y-$coordinate $y=-\sqrt[\phantom{2}]{\frac{9}{4}},$ or$,$ equivalently, $y=-\frac{3}{2}.$ The other point has the $y-$copreinate $y=\frac{3}{2}$

To conclude, state the two points.

smaller $y-$value $,(x,y)=()$

Iarger $y-$value $,(x,y)=()$