Analytic geometry elliptic problem: elliptic equation x ^ 2 + 1 / 2Y ^ 2 = 1, straight line y = x + B, there are two points on the ellipse symmetrical about the straight line, find the value range of B So x1-y1 + B = x2-y2 + B or x1-y1 + B = - (x2-y2 + b) That is, x1-x2 = y1-y2 or X1 + x2 = Y1 + Y2 How to x1-y1 + B = - (x2-y2 + b) to X1 + x2 = Y1 + Y2 2b is gone?

Analytic geometry elliptic problem: elliptic equation x ^ 2 + 1 / 2Y ^ 2 = 1, straight line y = x + B, there are two points on the ellipse symmetrical about the straight line, find the value range of B So x1-y1 + B = x2-y2 + B or x1-y1 + B = - (x2-y2 + b) That is, x1-x2 = y1-y2 or X1 + x2 = Y1 + Y2 How to x1-y1 + B = - (x2-y2 + b) to X1 + x2 = Y1 + Y2 2b is gone?

Suppose there are two points (x1, Y1), (X2, Y2) on the ellipse, then the above two points are substituted into the elliptic equation respectively. By making difference between the two equations (point difference method), we get {(x1 + x2) (x1-x2)} / {(Y1 + Y2) (y1-y2)} = - 1 / 2 because (x1-x2) / (y1-y2) = 1 / K, so (x1 + x2) / K (Y1 + Y2) = - 1 / 2 because these two points are related to the straight line y =