Through two points (- 1,1 / 2) on the parabola x ^ 2 = 2Y, B (2,2) respectively make the tangent line of the parabola, and the two tangent lines intersect at point M Verification ∠ BAM = ∠ BMA

Let am's equation be Y-1 / 2 = K1 (x + 1) and BM's equation be Y-2 = K2 (X-2). Substituting into the parabolic equation, we get respectively x ^ 2-2k1x - (2K1 + 1) = 0, (2K1) ^ 2 + 4 (2K1 + 1) = 0, K1 = - 1. X ^ 2-2k2x + 4 (k2-1) = 0, (2k2) ^ 2-16 (k2-1) = 0, K2 = 2. Two tangents intersect at (1 / 2, - 1). AB ^ 2 = BM ^ 2 = 45 / 4

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