Isoptic curves of a parabola

  • Drag the point on the red isoptic curve and check if the angle between the tangents to the parabola does not change.
  • Change the angle by using the slider. For right angle you will get the directrix of the parabola as the isoptic curve, for other values we obtain a hyperbola: the two branches of the hyperbola correspond to supplementary angles. Therefore the hyperbola is called a bisoptic curve.
  • You may also change the initial algebraic curve on the top-left. Caution: higher order functions may be too heavy to compute.
This is a joint work with Thierry Noah Dana-Picard.