Elliptic equation x ^ 2 / 4 + y ^ 2 / 3 = 1, try to determine the value range of T, so that there are two different points on the ellipse symmetrical about the straight line y = 4x + t

Elliptic equation x ^ 2 / 4 + y ^ 2 / 3 = 1, try to determine the value range of T, so that there are two different points on the ellipse symmetrical about the straight line y = 4x + t

Let these two points be m (x1, Y1) n (X2, Y2) Mn midpoint (x0, Y0) (x1) ^ 2 / 4 + (Y1) ^ 2 / 3 = 1 (x2) ^ 2 / 4 + (Y2) ^ 2 / 3 = 1. Subtract the two expressions to get (x1 + x2) / (Y1 + Y2) = - 4 / 3 * (y2-y1) / (x2-x1). Notice that (x1 + x2) / (Y1 + Y2) = x0 / Y0 (y2-y1) / (x2-x1) = - 1 / 4, so x0 / Y0 = 1 / 3 and Y0 = 4x0 + T to get x0