I have an unusual problem. I want to know the ratio of the height of an ellipse from either focus compared with the height of the ellipse at the centre, as the distance between the foci tends to infinity. When the distance between the foci tends to zero, the height above (below) the foci tends to the height at the centre because the foci tend to the centre. But I'm wondering if, as the distance tends to infinity, the foci height tends to half the centre height. Any help greatly appreciated - this matter has philosophical import!!!