Polar Curve Asymptotes:

Let the equation of a polar curve be shown as 1/r= ƒ(θ). Let α be a root of ƒ(θ) = 0. Then r sin (θ - 1/ƒ'(α))=is an asymptote of the curve.

Proof: Let P (r, θ) be any arbitrary point on the provided curve. We have
 

Clearly P leads to infinity along the curve of r->∞.

Since α is a root of ƒ(θ) = 0, it follows that θ ->α as r->∞.

Now

 

Therefore the required asymptote y = mx + c becomes

 

is an asymptote of the curve.