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The article presents geometrical proofs of properties of ellipses. Properties mentioned include two intersection points and the intersection point of the directrices corresponding to the common focus are collinear, intersection point of the other pair of directrices is collinear with the three points in case of ellipses with equal major semi-axes, and common focus belongs to the same line in case of identical conics. also discussed are three collinear points.

The article explores the transformation of a foci of a conic section becomes a strophoid as the axis of the plane rotates. It mentions that a classical outcome produces the locus of the foci as an oblique strophoid when the plane moves about a tangent to the cone. Also, it analyzes a family of curves observed as the axis of rotation moves.

The article analyzes the consequences of modifying the common definition of a parabola by studying the locus of all points equidistant from a focus and directrix. By generalizing the directrix, the analysis demonstrates that the conic sections are generalized parabolas whose directrix is a circle or a line. Also, it shows that the reflective properties of the conic sections are particular examples of a reflective property held by all generalized parabolas.

The article illustrates a mathematical equation on ball dynamics on a planet and the comparison of its gravity to two rotating spacecrafts. If a ball is thrown to the earth from Asteriod B-612 which is 35 feet in diameter and has the same gravity as the moon, it would follow a path of parabolic shape. If the ball moves too fast, the parabolic shape and flat earth model breaks down since downward acceleration is not constant and the earth is curved. Following the principles of scientists Isaac Newton and Johannes Kepler, a ball that is thrown so fast follows a parabolic, hyperbolic or elliptical path. If a ball is thrown from spaceship Discovery, with sphere of 40 feet in diameter, air resistance is ignored and the mass of the space station does not affect the motion of the ball.

The article discusses the methods of constructing a parabola discovered by Leah Berman who received her doctorate from the University of Washington. She was introduced to the method of constructing a parabola during a minicourse on origami conducted at the 2004 Mathematics Meetings led by Thomas Hull. She identified steps on how to form conics by means of folding. She also wrote a discussion of the construction of envelopes adapted from several references which described how to compute envelopes.

The article discusses mathematician Archimedes' quadrature of the parabola. In the quadrature of the parabola he found the area of the region bounded by a parabola and a chord. Archimedes' method involved filling the region with infinitely many triangles each of whose area he could calculate and then to evaluate the infinite sum. A parabolic segment consists of the region bounded by a parabola and the line segment joining two of its points B' and B. The motion of a particle in a uniform gravitational field is used to study the properties of the parabolic curve. Archimedes' Theorem states that the area of a parabolic segment is 4/3 the area of its Archimedean triangle. It was assumed that the infinity of smaller and smaller triangles fill the parabolic segment.

Discusses the problem of the relative position of the Euler line relative to the triangle. Introduction of notations to denote the lengths of the sides; Proof of an inequality in any acute triangle; Visualization of the ellipse between the perpendicular lines.

Focuses on the tangent lines of a conic selection. Reference to the work of Mikko Stenlund on parabolas; Inadequacy of certain features of the bisection theorem; Form of the curve; Elimination of the tangent angle; Characterization of a conic section.

Discusses a method of calculating the eccentricity of a conic section. Definition of the conic section by general quadratic equation; Equation for an ellipse; Distance between a focus of the ellipse and its center; Equation for deriving eccentricity.

This article presents mathematical insights and effective teaching strategies for college mathematics instruction. It discusses an area approach to the second derivative. It defines the second derivative of a function and other possible definition. It presents the formula for the second derivative that involves areas. In addition, a characterization of parabolas is also presented. In the case when the function is a parabola, a calculation is presented and the geometric calculation may have been known to the ancient Greeks.

Presents a mathematical problem that uses the vertex formula for a parabola. Accounts on the actual steps to produce a maximum value for the continuous model in algebra courses; Importance of a careful interpretation of the numerical results; Consideration of the continuous function of the curve.

The article reports on the geometric proof for the fact that a conic section, if it is a closed curve, satisfies the equation of an ellipse by using Cartesian coordinate system and geometric mean theorem to the right triangles.

This article presents a study regarding the conic sections from the plane point of view. It provides an analytic proof that the conic sections are found by cutting a cone at different angles. The proof does not require spheres or circles, but primarily depends on the cutting plane itself. It also presents a two-snapped circular cone which may be viewed as the result of rotating the line generator about the fixed line while maintaining the same angle. The equation for the circular cone is also presented.

Describes the usual way to find the equation of a tangent line to a general conic section at a point depends upon implicit differentiation. Emphasis on the intuitive definition of a tangent to a curve; Cancellation of the second degree terms of yields; Assumption on the absence of calculus.

The article reviews the article "Groups Associated with Conics," by Shailesh A. Shirali, which appeared in the periodical "The Mathematical Gazette" in March 2009.

Solicits an anomaly regarding the general equation of the non-slant conic section. Derivation of the equation; Nine points determining it; Illustration of the graph.