Question

高等数学 已知这个方程组，怎么化为参数方程啊？

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Answer 1

z = 1-x
x^2+y^2+(1-x)^2 = 9/2
2x^2-2x+y^2 = 7/2
2(x-1/2)^2+y^2 = 4
(x-1/2)^2/2+y^2/4 = 1
令 x = √2cost+1/2
y = 2sint
则 z = 1-x = -√2cost +1/2
故参数方程是 x = √2cost+1/2，y = 2sint，z = -√2cost +1/2

Answer 2

z = 1-x
x^2+y^2+(1-x)^2 = 9/2
2x^2-2x+y^2 = 7/2
2(x-1/2)^2+y^2 = 4
(x-1/2)^2/2+y^2/4 = 1
令 x = √2cost+1/2
y = 2sint
则 z = 1-x = -√2cost +1/2
故参数方程是 x = √2cost+1/2，y = 2sint，z = -√2cost +1/2