The auxiliary circle $x^2$ + $y^2$ = $a^2$ circumscribes the ellipse; every point on the ellipse has a corresponding point on the auxiliary circle at the same eccentric angle. The ratio of the ellipse area to the auxiliary circle area is b/a. The director circle $x^2$ + $y^2$ = $a^2$ + $b^2$ is the locus of points from which perpendicular tangents can be drawn. Its radius sqrt($a^2$ + $b^2$) is always greater than a. For any point on the director circle, the two tangents to the ellipse are perpendicular. This is the analog of the parabola's directrix being the locus of perpendicular tangent intersections, but here the locus is a circle (not a line) because the ellipse has finite extent.