Area Equation Of Conic Curve And Design Of Lesson Plans About It

The topic of Conic sections is the fundaental content in plane analytical geometry at school level. Any properties of conic sections have great significance for our study and life, so this paper focuses on the propositions of the area equation of conic sections in Apollonius of Perga Conics.First of all,the author reanalyzes the relationship between these propositions.According to the number of points on the curve,the author divides the twenty propositions involved from the shallower to the deeper into three categories of natures.The first kind of natures is that the area of two triangles made by the diameters and tangents are equal, including the proposition 1,4,13 of third volume.Second kind of natures is that the area of a triangle and a quadrilateral made by the diameters and tangents are equal, including the proposition 42,43,44,45 of first volume and the proposition 2,5,6,11,14,15 of third volume. Third kind of natures is that he area of two quadrilaterals made by the diameters and tangents are equal, including the proposition 3,7,8,9,10,12 of third volume. Then the author makes these propositions graph in the rectangular coordinate system, and through the analytic geometry method to prove these properties.Finally, in the basis of existing knowledge of conic of high school students, the author designs the lesson plan that is based on first nature to high school students show the properties.High school students can understand the nature of the first nature and aster mathematical methods in the process of proof.lt can provide new materials for students to learn the conics and broaden students' horizons.