✔ 最佳答案
(1) Let the points be (x,y)
√[x^2 + (y - 1)^2] + √(x^2 + (y + 5)^2] = 8
√[x^2 + y^2 - 2y + 1] = 8 - √(x^2 + y^2 + 10y + 25]
x^2 + y^2 - 2y + 1 = 64 - 16√(x^2 + y^2 + 10y + 25] + x^2 + y^2 + 10y + 25
12y + 24 + 64 = 16√(x^2 + y^2 + 10y + 25]
3y + 22 = 4√(x^2 + y^2 + 10y + 25]
(3y + 22)^2 = 16(x^2 + y^2 + 10y + 25)
9y^2 + 132y + 484 = 16x^2 + 16y^2 + 160y + 400
16x^2 + 7y^2 + 28 + 28 = 112
16x^2 + 7(y + 2)^2 = 112
x^2/7 + (y+2)^2/16 = 1
(2) {[3(2x-8)^(1/3)]-[(x+2)(2x-8)^(-2/3)]}/[(2x-8)^(2/3)]
= [3(2x-8)^(1/3)]/[(2x-8)^(2/3)] - [(x+2)(2x-8)^(-2/3)]/[(2x-8)^(2/3)]
= 3(2x-8)^(-1/3) - (x+2)(2x-8)^(-4/3)
= (2x-8)^(-4/3)[3(2x-8) - (x+2)]
= (2x-8)^(-4/3)(5x - 26)
= (5x-26)/(2x-8)^(4/3)
(3) [e^(-ln x)]/[(ln e^(2x))+(ln e ^(3x)]
= (1/x) / (2x + 3x)= 1/5x^2
2010-01-13 23:15:33 補充：
唔好意思,係打錯,應該係: 16x^2 + 7y^2 + 28y + 28 = 112漏左個y
9y^2 + 132y + 484 = 16x^2 + 16y^2 + 160y + 400
16x^2 + 7y^2 + 28y = 84
16x^2 + 7y^2 + 28y + 28 = 84 + 28 (completing square for y)
16x^2 + 7(y^2 + 4y + 4) = 112
16x^2 + 7(y + 2)^2 = 112
16x^2/112 + 7(y+2)^2 / 112 = 112/112
x^2/7 + (y+2)^2/16 = 1
