题目
题型:不详难度:来源:
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(Ⅰ)求曲线C普通方程;
(Ⅱ)若点A(ρ1,θ),B(ρ2,θ+
2π |
3 |
4π |
3 |
1 |
|OA|2 |
1 |
|OB|2 |
1 |
|OC|2 |
答案
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∵曲线C的参数方程是
|
x2 |
a2 |
y2 |
3 |
把点(2,0)代入上述方程得a=2.
∴曲线C普通方程为
x2 |
4 |
y2 |
3 |
(Ⅱ)∵点A(ρ1,θ),B(ρ2,θ+
2π |
3 |
4π |
3 |
2π |
3 |
2π |
3 |
4π |
3 |
4π |
3 |
∴
1 |
|OA|2 |
1 |
|OB|2 |
1 |
|OC|2 |
1 |
ρ12 |
1 |
ρ22 |
1 |
ρ32 |
1 |
4 |
2π |
3 |
4π |
3 |
1 |
3 |
2π |
3 |
4π |
3 |
=
1 |
4 |
1+cos2θ |
2 |
1+cos(2θ+
| ||
2 |
1+cos(2θ+
| ||
2 |
1 |
3 |
1-cos2θ |
2 |
1-cos(2θ+
| ||
2 |
1-cos(2θ+
| ||
2 |
=
3+cos2θ-cso(2θ+
| ||||
8 |
3-cos2θ+cos(2θ+
| ||||
6 |
=
3 |
8 |
3 |
6 |
7 |
8 |
核心考点
试题【(选修4-4:坐标系与参数方程)已知曲线C的参数方程是x=acosφy=3sinφ(φ为参数,a>0),直线l的参数方程是x=3+ty=-1-t(t为参数),曲】;主要考察你对极坐标与直角坐标等知识点的理解。[详细]
举一反三
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|
π |
3 |