Question

已知直线L的极坐标方程为ρsin（θ-π/3）=6，圆C的参数方程为x=10cosθ y=10sinθ

Answer 1

(2)
ρ
=
√(x^2
+
y^2)
cosθ=x/√(x^2
+
y^2),
sinθ
=
y/√(x^2
+
y^2)
ρsin（θ-π/3）=6
√(x^2
+
y^2)[sinθcos(π/3)
-
cosθsin(π/3)]
=
6
√(x^2
+
y^2)[(1/2)sinθ
-
(√3/2)cosθ]
=
6
√(x^2
+
y^2)[sinθ
-
√3cosθ]
=
12
√(x^2
+
y^2)[
y/√(x^2
+
y^2)
-
√3x/√(x^2
+
y^2)]
=
12
y
-
√3x
=
12
√3x
-
y
+
12
=
0
(2)
x^2
+
y^2
=
(10cosθ)^2
+
(10sinθ)^2
=
100[(cosθ)^2
+
(sinθ)^2]
=
100
x^2
+
y^2
=
100
圆半径r=10,
圆心与√3x
-
y
+
12
=
0的距离d
=
|√3*0
-
0
+
12|/√4
=
6
直线L被圆截得的弦长
=
2√(r^2
-
d^2)
=
2*8
=
16