Tangents to conic sections

• Main Author: Reneau, Lorean Nicole
• Format: Others
• Language: English
• Published: 2011
• Subjects: Tangent; Conic sections; Ellipses; Hyperbolas; Dandelin spheres
• Online Access: http://hdl.handle.net/2152/ETD-UT-2010-08-1607

Circles, parabolas, ellipses and hyperbolas are conic sections and have many unique properties. The properties of the tangents to conic sections prove quite interesting. Dandelin spheres are tangent to ellipses inside a cone and support the geometric definition of an ellipse. Tangent lines to parabolas, ellipses and hyperbolas in the form of families of folds are shown to create conic sections in unique ways. The equations of these tangent lines to conic sections and their equations can be found without using calculus. The equations of the tangent lines are also used to prove the bisection theorem for all conic sections and prove uniqueness for the bisection theorem in connection to conic sections. === text