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An isoptic curve formed from the locus of tangents meeting at right angles. The orthoptic of a parabola is its conic section directrix. The orthoptic of a central conic was ...

The outer Soddy center (or outer Soddy point) is the center of the outer Soddy circle. It is equivalent to the isoperimetric point X_(176) (Kimberling 1994) and has ...

The catacaustic of a parabola (t,t^2) opening upward is complicated for a general radiant point (x,y). However, the equations simplify substantially in the case x=infty ...

A curve named and studied by Newton in 1701 and contained in his classification of cubic curves. It had been studied earlier by L'Hospital and Huygens in 1692 (MacTutor ...

A quartic curve with implicit equation (a^2)/(x^2)-(b^2)/(y^2)=1 (1) or a^2y^2-b^2x^2=x^2y^2 (2) and a,b>0. In parametric form, x = +/-acost (3) y = bcott. (4) The curvature ...

A set of planes sharing a point in common. For planes specified in Hessian normal form, a bundle of planes can therefore be specified as ...

The envelope of the lines connecting corresponding points on the Jacobian curve and Steinerian curve. The Cayleyian curve of a net of curves of order n has the same curve ...

The envelope of refracted rays for a given curve.

Given positive numbers s_a, s_b, and s_c, the Elkies point is the unique point Y in the interior of a triangle DeltaABC such that the respective inradii r_a, r_b, r_c of the ...

The inverse curve of Fermat's spiral with the origin taken as the inversion center is the lituus.