Question

證明過A(ρ₁,θ₁)和B(ρ₂,θ₂)兩點的直線l的極坐標方程是.

Answer 1

證明:設(shè)M(ρ,θ)為直線AB上一點,如圖,

∵S_△AOB=ρ₁ρ₂sin(θ₂-θ₁),

S_△AOM=ρρ₁sin(θ-θ₁),

S_△BOM=ρρ₂sin(θ₂-θ),

又S_△AOB=S_△AOM+S_△BOM,

∴ρ₁ρ₂sin(θ₂-θ₁)=ρρ₁sin(θ-θ₁)+ρρ₂sin(θ₂-θ),

即.