Curve Tracing f(r,θ)=0

Symmetry #

• If f(r,θ)=f(r,A-θ), then the curve is symmetric wrt θ=A/2
• If f(-r,θ)=f(r,θ), then curve is symmetric wrt pole (r=0).

Pole #

Curve passes through pole if there’s a θ₀ for which r=0: i.e. if for f(0,θ₀)=0, a solution exists.

Tangent at Pole #

θ=θ₀ is tangent at pole iff f(0,θ₀)=0.

Table #

We make a table of (r,θ) in order to plot some points on the curve.

Asymptote #

If f(∞,θ₀)=0 as θ approaches θ₀, θ=θ₀ is the asymptote

Tangent at other point #

dy/dx=tan(θ₀)=$\frac{r(θ)}{r’(θ)}$