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設該兩條切線與曲線切於(a, b) 9x2 + 16y2 = 52 18x + 32y*dy/dx = 0 dy/dx = -9x/16y dy/dx |(a, b) = -9a/16b 所需切線的斜率 = 9/8 -9a/16b = 9/8 -a/2b = 1 a = -2b 而且, 9a2+ 16b2 = 52 9(-2b)2 + 16b2 = 52 52b2 = 52 b2 = 1 b = 1 或 b = -1 當b = 1, a = -2, 切線方程: y﹣1 = (9/8)(x+2), 即是9x﹣8y+26 = 0 當b = -1, a = 2, 切線方程: y+2 = (9/8)(x﹣2), 即是9x﹣8y﹣26 = 0
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求曲線9x^2+16y^2=52的兩條切線方程,其中該兩條切線都平行於直線9x-8y-2=0最佳解答:
設該兩條切線與曲線切於(a, b) 9x2 + 16y2 = 52 18x + 32y*dy/dx = 0 dy/dx = -9x/16y dy/dx |(a, b) = -9a/16b 所需切線的斜率 = 9/8 -9a/16b = 9/8 -a/2b = 1 a = -2b 而且, 9a2+ 16b2 = 52 9(-2b)2 + 16b2 = 52 52b2 = 52 b2 = 1 b = 1 或 b = -1 當b = 1, a = -2, 切線方程: y﹣1 = (9/8)(x+2), 即是9x﹣8y+26 = 0 當b = -1, a = 2, 切線方程: y+2 = (9/8)(x﹣2), 即是9x﹣8y﹣26 = 0
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