Do It Yourself

3264 conics in a second.

A conic in the plane $\mathbb{R}^2$ is the zero set of a quadratic polynomial in two variables:

$$\,\, a_1 x^2 \,+\, a_2 xy \,+\, a_3 y^2 \, +\, a_4 x \, + \, a_5 y \, + \, a_6 \,.$$

Geometrically, a conic can be either a circle, an ellipse, a hyperbola, a parabola or a union of two lines. The last case is called a degenerate conic.

Steiner’s conic problem asks the question of how many conics are tangent to five given conics. This webpage gives an answer to a slightly different question:

Which conics are tangent to your five conics?

Plug in the coefficients of your five personal conics, and get the answers in a second (your conics must be sufficiently generic in the sense that the 3264 complex conics tangent to your five conics are all isolated; in particular, degenerate conics are not allowed).


More information on how this works can be found in the article 3264 conics in a Second.


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