Do you mean a closed set in the usual topology on ? If so, is its complement open? That is, if you take a point (x, y) NOT satisfying that equation, must there be a (possibly very small) neighborhood about it that is also not in the set.

If (x,y) is not on the ellipse, draw a line from (x,y) perpendicular to the ellipse. That is the shortest distance from the point to the ellipse. What about a disk centered on (x, y) with radius half that distance?

I don't use mathlab but if you asked it to graph and then it was "complaining" about x values larger than and x values less than . That is, outside the ellipse.

Yes, thisisan ellipse- its "standard form" would be