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设切点B(a, b): a² + b² = 4 (1)
OB⊥AB, 二者斜率分别为b/a, (b - 4)/(a - 2)
(b/a)[(b - 4)/(a - 2)] = -1
a = 2 -2b (2)
代入(1): b = 0 (a = 2)或b = 8/5 (a = -6/5)
切线方程:
B(2, 0), x = 2
B(-6/5, 8/5): (y - 8/5)/(4 - 8/5) = (x + 6/5)/(2 + 6/5), 15x - 20y + 50 = 0
AB = √(OA² - OB²) = √(2² + 4² - 4) = 4
OB⊥AB, 二者斜率分别为b/a, (b - 4)/(a - 2)
(b/a)[(b - 4)/(a - 2)] = -1
a = 2 -2b (2)
代入(1): b = 0 (a = 2)或b = 8/5 (a = -6/5)
切线方程:
B(2, 0), x = 2
B(-6/5, 8/5): (y - 8/5)/(4 - 8/5) = (x + 6/5)/(2 + 6/5), 15x - 20y + 50 = 0
AB = √(OA² - OB²) = √(2² + 4² - 4) = 4
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