We recall the notion of generalized hyperbolic angle between proper and improper straight lines, which is only available in Hungarian and Esperanto. Then we summarize the generalized hyperbolic conic sections. After the investigation of real conic sections and their isoptic curves in the hyperbolic plane H 2 , we consider the problem of isoptic curves of generalized conic sections in the extended hyperbolic plane. This problem is widely investigated in the Euclidean plane E 2 but, in the hyperbolic and elliptic planes, there are few results. Furthermore, we determine and visualize the generalized isoptic curves to all hyperbolic conic sections. For our computations, we use the classical models based on the projective interpretation of hyperbolic geometry. In this way, the isoptic curves can be visualized in the Euclidean screen of a computer.

中文翻译：

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双曲平面内广义圆锥截面的等视曲线

我们回忆一下正确和不正确直线之间的广义双曲角的概念，该概念仅在匈牙利语和世界语中可用。然后我们总结了广义双曲圆锥截面。在研究了双曲平面H 2 内的实圆锥截面及其等光曲线之后，我们考虑了扩展双曲平面内广义圆锥截面的等光曲线问题。这个问题在欧几里得平面 E 2 中得到了广泛研究，但在双曲平面和椭圆平面中，结果很少。此外，我们确定和可视化所有双曲圆锥截面的广义等光曲线。对于我们的计算，我们使用基于双曲几何投影解释的经典模型。这样，等光曲线可以在计算机的欧几里得屏幕上可视化。