Construction of dandelin sphere on definition of conics using geogebra classic 5

Abstract

Conics is a curve formed by the intersection of a plane with a cone. The types of conics depend on the relationship of angle between the axis of the cone and the angle between the cutting plane with one of the generating line. The conics can also be defined in terms of the eccentricity. The problem is when conics are defined as the intersection of a cone and a plane, it does not show the focus and directrix and when conics are defined by the eccentricity, it does not show that the conics are formed by the intersection of a cone and a plane. Germinal Pieree Dandelin finds the way to show that these definitions are related. He uses sphere of certain size and position inscribed inside to the cone. The purpose of this paper is to construct Dandelin sphere to show that the definition of conics are related each other. The construction steps are using GeoGebra Classic 5. The result shows that by dragging the cutting plane the type of the conics are formed and show where the focus point and directrix line are.