$We$ have determined that a point $on$ the given ellipse with $anx-$coordinate $x=\frac{1}{2}$ will $be$ the farthest possible

distance away from the point $(-1,0).To$ determine the $y-$coordinate $of$ such a point, $we$ use the substitution

$x=\frac{1}{2}in$ the equation $of$ the ellipse and solve for $y.$ Doing $so$ give the following.

Since there are two values $ofy$ for $x=\frac{1}{2},$ this indicates that there are

points $on$ the ellipse that

are $of$ maximum distance from the point $(-1,0).$