Given the hyperbola c1:2x ^ 2-y ^ 2 = 1, let the ellipse c2:4x ^ 2 + y ^ 2 = 1, if M and N are the moving points on C1 and C2 respectively, and OM is perpendicular to on, we prove that: The distance from O to the straight line Mn is a fixed value

Given the hyperbola c1:2x ^ 2-y ^ 2 = 1, let the ellipse c2:4x ^ 2 + y ^ 2 = 1, if M and N are the moving points on C1 and C2 respectively, and OM is perpendicular to on, we prove that: The distance from O to the straight line Mn is a fixed value

Let om length R1, on length R2 and the angle between OM and X axis be a, then the angle between on and X axis is a + π / 2m: (r1cosa, r1sina); then n (r2cos (a + π / 2); r2cos (a + π / 2)); n coordinate is equivalent to (- r2sina, r1cosa) substituting C1, c2r1 ^ 2 * (2 (COSA) ^ 2 - (Sina) ^ 2) = 1