Thesis (Design) Title Some Properties of Tangents of Conic Curves and Their Applications
Department (College) Mathematics and Applied Mathematics 09 Series (II) Subject Science
Name of Student Cheng Jun Instructor Xu Quannian
Professor with academic number 0925809070
1. Selection basis (1). The content includes: the source and significance of the topic, the research status at home and abroad, the research goal of this topic, the content innovation and the main references. 2. Writing requirements: Song Ti and Xiao Si. ) 1. The source and significance of the topic Conic curve is the core content of plane analytic geometry, and it is also the key and difficult point of high school mathematics, so it has become an essential test content in the college entrance examination. One of the main contents of conic curve is related to the tangent of conic curve, although this kind of problem is not discussed in depth in the textbook. However, problems related to the tangent of conic curve often appear in exams. However, most of the research in this field in domestic and foreign literature only gives abstract properties and proofs, and rarely gives relevant applications of properties, so it is difficult for students to use these properties flexibly when dealing with specific problems. Therefore, this topic has very important practical value and significance. 2. Research situation at home and abroad According to the known information in the current reference moral literature, in recent years, researchers have discussed the properties of the tangent of the conic curve from their own perspectives and obtained a series of results. For example, in Zhang's article "Proof and generalization of a property of conic curve", the relationship between any point on a quasi-straight line and the two ends of focus chord and the nature of the slope of the straight line where focus chord is located are obtained. In the article "A Property of the Tangent of a Conic Curve", Zhou Weilin obtained the general property of the tangent of a conic curve. In the paper Geometric Characteristics of Conic Curve, Huang Yan created the intrinsic properties of tangent and symmetry axis of conic curve and triangle with vertex on conic curve. Wu obtained the property of tangent length in the paper Generalization of Important Properties of Circle on Conic Curve. Jeffrey Chang obtained the property of the relationship between tangent and secant in the article "A Property of Conic Curve". In the article "The Properties and Applications of Quadratic Curve", Pandang obtained the properties and applications of the relationship between the focal point, the directrix and the tangent of the conic. 3. The research goal is to reveal the hidden unified characteristics of conic curve by discussing the related properties and applications of drawing two tangents and secants from a point outside the conic curve, and drawing a tangent and a normal passing through this point. 4. The innovation of this paper is based on the existing literature. By introducing two tangent lines and two secant lines from a point outside the conic, and introducing a tangent line and a normal line passing through this point, the tangent line of the conic is studied, and five properties of the tangent line of the conic are obtained, and the unified properties of the hidden tangent line of the conic are revealed by applying these properties. 5. [1] Zheng mainly refers to it. A generality of conic curve.