极坐标方程ρ=2sin(θ-π /4) 表示的曲线是?
2个回答

ρ=2sin(θ-π/4)

ρ^2=2ρsin(θ-π/4)

x^2 + y^2 = 2ρsinθcosπ/4-2ρcosθsinπ/4

x^2 + y^2 = √2ρsinθ - √2ρcosθ

x^2 + y^2= √2y - √2x

x^2 + √2x + y^2 - √2y =0

x^2 + √2x + 1/2 + y^2 - √2y +1/2 =1

(x+1/√2)^2 + (y-1/√2)^2 = 1

即圆心(-1/√2,1/√2)半径为1的圆

√2:2开平方 π 圆周率

应用公式:ρ^2 = x^2 + y^2

x=ρcosθ y=ρsinθ