试用参数方程
来源:学生作业帮 编辑:搜搜考试网作业帮 分类:数学作业 时间:2024/07/27 19:44:07
试用参数方程
![](http://img.wesiedu.com/upload/f/d8/fd80d1d251ac18c9afb340d14c7094e2.jpg)
![](http://img.wesiedu.com/upload/f/d8/fd80d1d251ac18c9afb340d14c7094e2.jpg)
![试用参数方程](/uploads/image/z/9152284-4-4.jpg?t=%E8%AF%95%E7%94%A8%E5%8F%82%E6%95%B0%E6%96%B9%E7%A8%8B)
将直角坐标系转换成极坐标,
以原点为极点,x轴正半轴为极轴,建立极坐标系.则椭圆方程为 ρ^2(cosθ)^2/a^2+ρ^2(sinθ)^2/b^2=1 (x=ρcosθ,y=ρsinθ)
设A(ρ1,φ),B(ρ2,φ+2π/3),C(ρ3,φ+4π/3),则 (cosφ)^2/a^2+(sinφ)^2/b^2=1/(ρ1)^2,(cosφ+2π/3)^2/a^2+(sinφ+2π/3)^2/b^2=1/(ρ2)^2,(cosφ+4π/3)^2/a^2+(sinφ+4π/3)^2/b^2=1/(ρ3)^2
所以 1/|OA|^2+1/|OB|^2+1/|OC|^2=(cosφ)^2/a^2+(sinφ)^2/b^2+(cosφ+2π/3)^2/a^2+(sinφ+2π/3)^2/b^2+,(cosφ+4π/3)^2/a^2+(sinφ+4π/3)^2/b^2
所以 1/|OA|^2+1/|OB|^2+1/|OC|^2=1.5/a^2+1.5/b^2
以原点为极点,x轴正半轴为极轴,建立极坐标系.则椭圆方程为 ρ^2(cosθ)^2/a^2+ρ^2(sinθ)^2/b^2=1 (x=ρcosθ,y=ρsinθ)
设A(ρ1,φ),B(ρ2,φ+2π/3),C(ρ3,φ+4π/3),则 (cosφ)^2/a^2+(sinφ)^2/b^2=1/(ρ1)^2,(cosφ+2π/3)^2/a^2+(sinφ+2π/3)^2/b^2=1/(ρ2)^2,(cosφ+4π/3)^2/a^2+(sinφ+4π/3)^2/b^2=1/(ρ3)^2
所以 1/|OA|^2+1/|OB|^2+1/|OC|^2=(cosφ)^2/a^2+(sinφ)^2/b^2+(cosφ+2π/3)^2/a^2+(sinφ+2π/3)^2/b^2+,(cosφ+4π/3)^2/a^2+(sinφ+4π/3)^2/b^2
所以 1/|OA|^2+1/|OB|^2+1/|OC|^2=1.5/a^2+1.5/b^2