標題:
關於微分應用的一條問題.
發問:
求曲線x^2-2y^2=7的兩條切線方程,其中該兩條切線都通過(-1,5) 答案為3x+2y-7=0和19x-6y+49=0.
求曲線x2-2y2=7的兩條切線方程,其中該兩條切線都通過(-1,5) for differentiating x2 - 2y2 = 7 both sides respect to x in order to find the implicit derivatives, x2 - 2y2 = 7 2x - 4y(dy/dx) = 0 dy/dx = x/2y hence,let (a,b) be the coordinates of that point,such that a2 - 2b2 = 7,and, b - 5 = (a/2b)(a + 1) a2 + a = 2b2 - 10b a2 - 2b2 = -(10b + a) as,10b + a = -7 a = -(10b + 7) sub into the equation a2 - 2b2 = 7 [-(10b + 7)]2 - 2b2 = 7 100b2 + 140b + 49 - 2b2 = 7 98b2 + 140b + 42 = 0 7b2 + 10b + 3 = 0 (7b + 3)(b + 1) = 0 b = -3/7 or b = -1 a = -19/7 or a = 3 the equation: 2(y + 3/7) = [(-19/7)/(3/7)](x + 19/7) or 2(y + 1) = (3/-1)(x - 3) 19x - 6y + 49 = 0 or 3x + 2y - 7 = 0
其他解答:
關於微分應用的一條問題.
發問:
求曲線x^2-2y^2=7的兩條切線方程,其中該兩條切線都通過(-1,5) 答案為3x+2y-7=0和19x-6y+49=0.
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最佳解答:求曲線x2-2y2=7的兩條切線方程,其中該兩條切線都通過(-1,5) for differentiating x2 - 2y2 = 7 both sides respect to x in order to find the implicit derivatives, x2 - 2y2 = 7 2x - 4y(dy/dx) = 0 dy/dx = x/2y hence,let (a,b) be the coordinates of that point,such that a2 - 2b2 = 7,and, b - 5 = (a/2b)(a + 1) a2 + a = 2b2 - 10b a2 - 2b2 = -(10b + a) as,10b + a = -7 a = -(10b + 7) sub into the equation a2 - 2b2 = 7 [-(10b + 7)]2 - 2b2 = 7 100b2 + 140b + 49 - 2b2 = 7 98b2 + 140b + 42 = 0 7b2 + 10b + 3 = 0 (7b + 3)(b + 1) = 0 b = -3/7 or b = -1 a = -19/7 or a = 3 the equation: 2(y + 3/7) = [(-19/7)/(3/7)](x + 19/7) or 2(y + 1) = (3/-1)(x - 3) 19x - 6y + 49 = 0 or 3x + 2y - 7 = 0
其他解答:
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