为ρ2=-2(ρcosθ-ρsinθ).
因为圆过极点,
所以方程可简化为ρ=2(sinθ-cosθ).
答案A
8(2018·天津模拟)在极坐标系中,点(√2 "," π/4)到直线ρcos θ-ρsin θ-1=0的距离等于________________________.
解析点(√2 "," π/4)的直角坐标为(1,1),直线ρcosθ-ρsinθ-1=0的直角坐标方程为x-y-1=0,点到直线的距离为 ("|" 1"-" 1"-" 1"|" )/√2=√2/2.
答案√2/2
9在极坐标系中,点P("-" 2"," π/2)到直线l:3ρcos θ-4ρsin θ=3的距离为 .
解析在相应的平面直角坐标系中,点P的坐标为(0,-2),直线l的方程为3x-4y-3=0,所以点P到直线l的距离d=("|" 3×0"-" 4×"(-" 2")-" 3"|" )/√(3^2+"(-" 4")" ^2 )=1.
答案1
10在极坐标系中,曲线C1为ρ(√2 cos θ+sin θ)=1,曲线C2为ρ=a(a>0).若曲线C1与C2的一个交点在极轴上,则a= .
解析ρ(√2 cosθ+sinθ)=1,即√2 ρcosθ+ρsinθ=1对应的直角坐标方程为√2 x+y-1=0,ρ=a(a>0)对应的直角坐标方程为x2+y2=a2.在√2 x+y-1=0中,令y=0,得x=√2/2,将(√2/2 "," 0)代入x2+y2=a2,得a=√2/2.
答案 √2/2
11求过点A(2"," π/4)且平行于极轴的直线的极坐标方程.
解如图,在直线l上任意取除点A外的一点M(ρ,θ),连接OA,OM,过点M作极轴的垂线交极轴于点H.
因为A(2"," π/4),所以|MH|=2sin π/4=√2.