Key to Robinsons New Geometry and Trigonometry, and Conic Sections and Analytical Geometry: With Some Additional Astronomical Problems; Designed for Teachers and Students by Horatio N. RobinsonExcerpt from Key to Robinsons New Geometry and Trigonometry, and Conic Sections and Analytical Geometry: With Some Additional Astronomical Problems; Designed for Teachers and Students
A key to a Text-book on the Higher Mathematics, if not a new creation, is by no means a common thing. And it is a question undecided in the minds of many, whether a Key to any mathematical work is an aid, or a hindrance to the teacher.
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Finding The Focus and Directrix of a Parabola
Definition Conic sections can be defined as the locus of point that moves so that the ratio of its distance from a fixed point called the focus to its distance from a fixed line called the directrix is constant. The constant ratio is called the eccentricity of the conic. Conic sections are obtained by passing a cutting plane to a right circular cone.
Horatio N. Robinson
Easy to understand math lessons on DVD. Try before you commit. This is a summary of the first 5 topics in this chapter: straight line, circle, parabola, ellipse and hyperbola. Don't miss the 3D interactive graph , where you can explore these conic sections by slicing a double cone. The equation of a line passing through a point x 1 , y 1 with slope m :. If we slice the double cone by a plane just touching one edge of the double cone, the intersection is a straight line , as shown.
Determine whether the given equation is an equation of the conic section. If so, identify the type of a conic section and its properties the vertex, the center, the radius, the semi-major and semi-minor axis, the eccentricity :. Determine the relative position of a straight line p and a circle k. If they have any intersection points, determine their coordinates :. Find the equation of an ellipse having the center at the origin of the coordinate system and passing through the points M [2 ; ] and N [6;0].
In this chapter, we will investigate the two-dimensional figures that are formed when a right circular cone is intersected by a plane. We will begin by studying each of three figures created in this manner. We will develop defining equations for each figure and then learn how to use these equations to solve a variety of problems. Conic sections are formed when a plane intersects two right circular cones aligned tip to tip and extending infinitely far in opposite directions, which we also call a cone. The way in which we slice the cone will determine the type of conic section formed at the intersection. A circle is formed by slicing a cone with a plane perpendicular to the axis of symmetry of the cone.
Analyt ic Geometry - Conic Sections. General equation of a circle with the center S p, q - translated circle.
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