Kappa

A plane algebraic curve of order four whose equation in Cartesian rectangular coordinates has the form

$$(x^2+y^2)y^2=a^2x^2;$$

and in polar coordinates:

$$\rho=a\operatorname{cotan}\phi.$$

The origin is a nodal point with coincident tangents $x=0$ (see Fig.). The asymptotes are the lines $y=\pm a$. It is related to the so-called nodes (cf. Node in geometry).

#### References[edit]

[1] |  A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)

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[a1] |  J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972)