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Conic sections

Conic sections are sets of solutions of equations formed by linear combinations of x^2, y^2, x, y, xy and 1 (quadratic functions in two variables). It is well know, that conics are determined by 5 points. Select the 5 points to create a conic section. Two points can be replaced by one point and a tangent line. Select the point and a line. The conic section will have a tangent in that point, which is parallel to the line.

Conic sections can also be determined by their formula. To do this, click on the conic section icon with the ctrl key, or use the menu entry in the functions menu. In the dialog, enter a quadratic expression q(x,y), which will define the conic section by q(x,y)=0. Make sure, the expression really defines a conic section! Otherwise, a conic section interpolating your function in some points in the plane will be generated. You must use the variables x and y. Zero sets of other functions can be generated with the user function tool. But only a conic section can be used for intersections, and to place points on it.

To edit the properties of the curve, click on it and use the normal properties dialog. Conics will display the defining formula as their value.

It is possible to bind points on conic sections, and to create intersections of conic sections with other objects.

Related topics: Object Properties, Points, Transparency, Functions and Curves

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