求答案，速解
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解决时间 2021-02-06 07:49
- 提问者网友：酱爆肉
- 2021-02-05 12:39
求答案，速解
最佳答案
- 五星知识达人网友：时间的尘埃
- 2021-02-05 13:32
(1)
易知此为圆(x - 1)² + y² = 3 (i)
x² + y² - 2x - 2 = 0
令x = ρcosθ, y = ρsinθ
(ρcosθ)² + (ρsinθ)² - 2ρcosθ - 2 = 0
ρ² - 2ρcosθ - 2 = 0
(2)
射线的方程为y = xtan(π/3) = √3x, x > 0
带入(i): (x - 1)² + 3x² = 3
2x² - 2x - 1 = (x - 1)(2x + 1) = 0
x = 1, A(1, √3)
ρcos(θ - π/6) = 3√3与θ = π/3联立:
ρcos(π/3 - π/6) = 3√3, ρ = 6
B的坐标为x = ρcos(π/3) = 6cos(π/3) = 3
y = ρsin(π/3) = 6sin(π/3) = 3√3
B(3, 3√3)
|AB| = √[(3 -1)² + (3√3 - √3)²] = 4
易知此为圆(x - 1)² + y² = 3 (i)
x² + y² - 2x - 2 = 0
令x = ρcosθ, y = ρsinθ
(ρcosθ)² + (ρsinθ)² - 2ρcosθ - 2 = 0
ρ² - 2ρcosθ - 2 = 0
(2)
射线的方程为y = xtan(π/3) = √3x, x > 0
带入(i): (x - 1)² + 3x² = 3
2x² - 2x - 1 = (x - 1)(2x + 1) = 0
x = 1, A(1, √3)
ρcos(θ - π/6) = 3√3与θ = π/3联立:
ρcos(π/3 - π/6) = 3√3, ρ = 6
B的坐标为x = ρcos(π/3) = 6cos(π/3) = 3
y = ρsin(π/3) = 6sin(π/3) = 3√3
B(3, 3√3)
|AB| = √[(3 -1)² + (3√3 - √3)²] = 4
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