Parabola

A parabola is the locus of a point which moves so that its distances from a fixed point (the locus) and a fixed straight line (the directrix) are the same.  Construct the parabola according to this definition by using the command "perpendicular bisector".

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Construct the parabola as an envelope of its tangents.

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Construct the pair of tangents from a given point to the parabola.

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Given a pair of tangents and the focus, construct the parabola.

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Given the focus, a tangent and the point of contact, construct the parabola.

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Construct a parabola tangent to a fixed circle having a fixed diameter as axis.

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Construct the graph of the quadratic polynomial passing through three given points no two of which have the same abscissa.

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Construct the graph of the cubic polynomial passing through four given points no two of which have the same abscissa.

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Given coefficients a,b,c,d, construct the graph of the cubic polynomial

ax3 + bx2 + cx + d

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Generalize the theorem of a chain of four tangential circles to the case of graphs of quadratic polynomials.