EJMT Abstract

In this paper, we extend the original locus problem discussed in an earlier paper. We are given two conic curves, denoted by E₁ and E₂, respectively. Point A is outside these two conic curves. We draw tangents from A to the two curves, E₁ and E₂, respectively. An equioptic curve for two ellipses is the locus of points A from which the two ellipses subtend equal viewing angles. In this paper, we shall see how a uniform scaling, shiftings, and uniform shear will affect the quasi-locus discussed in this paper. We further explore the equioptics for infinitely many circles in 2D within an evenly divided circle in a given circle. We extend this to corresponding 3D to visualize the equioptics for infinitely many spheres within an evenly divided cone in a given sphere. It is clear that without the help of a computer algebra system, it is impossible to compute and visualize the equioptics described in this paper.