Question

将极坐标方程转换成直角方程（1）ρ+6cotθ/sinθ=0,（2)ρ=6/(1-2cosθ)

Answer 1

(1)

ρ+6cotθ/sinθ=0

ρsinθ + 6cotθ=0

y + 6/tanθ = 0

y + 6/(y/x) = 0

y² + 6x = 0

(2)

ρ(1 - 2cosθ) = 6

ρ - 2ρcosθ) = 6

√(x² + y²) - 2x = 6

x² + y² = 4x² + 24x + 36

3x² + 24x + 36 - y² = 0

(x + 4)²/4 - y²/12 = 1