It is proved that the line passing through the right focus F of the ellipse intersects with the ellipse at a and B, and when the line is perpendicular to the X axis | ab | is the shortest It is proved that the line passing through the right focus F of the ellipse x ^ 2 + 4Y ^ 2 = 4 intersects the ellipse at a and B, and | ab | is the shortest when the line is perpendicular to the X axis Please prove that, in fact, when it is not vertical, | ab | > 1

It is proved that the line passing through the right focus F of the ellipse intersects with the ellipse at a and B, and when the line is perpendicular to the X axis | ab | is the shortest It is proved that the line passing through the right focus F of the ellipse x ^ 2 + 4Y ^ 2 = 4 intersects the ellipse at a and B, and | ab | is the shortest when the line is perpendicular to the X axis Please prove that, in fact, when it is not vertical, | ab | > 1

A = 2, C = radical 3, let the ellipse intersected by a straight line passing through the right focus and two points, and the abscissa are X1 and X2 respectively. According to the focal radius formula a-ex0, we know that the distance from the ellipse to the focus is 2-half radical 3 x1, 2-half radical 3 x2 respectively. The length of the line segment: | ab | = 4-2 radical 3 (x1 + x2) let the straight line be y = K (x-radical 3) and