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Instructional Unit The Conics By: Diana Brown Introduction There are four mathematical curves that can be found in a cone, and these curves are called The Conics, or The Conic Sections. The four conic sections, circle, ellipse, parabola, hyperbola can be seen as slices of a cone. If the cone is sliced parallel to the base, the resulting curve is a circle. If the cone is sliced on a slight angle, the curve is called an ellipse. If the slice is made parallel to the edge of the cone, the curve formed is called a parabola. If the slice is perpendicular to the base of the cone, the curve is one of two branches of a hyperbola. Mathematicians are interested in two branches of the hyperbola, formed by putting two cones together. Diagram of Conics as represented above:
Real world representations of conics We see cones around us every day: ice cream cones, traffic cones, and cone-shaped sushi Ellipse: The orbits of the planets are elliptical and the earth itself is an ellipsoid. A circle viewed from an angle looks like an ellipse. Parabola: The parabola is the path followed by a thrown ball or by a spout of water in a fountain. Upside down parabolas are seen in some suspension bridges. Hyperbola: The pattern of light cast on a wall by a lampshade is a hyperbola. More real world representations of conics 
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Explanation: When the plane cuts the cone at an angle parallel to the axis of the cone, then the resulting conic section is called as a hyperbola. If the plane cuts the cone at an angle with respect to the axis of the cone then the resulting conic sections are called as ellipse and parabola. 7. Which conic section do you get when you cut the cone parallel to its axis?Cutting parallel to a side of the cone produces a parabola. Cutting more nearly parallel to the axis than to the side produces a hyperbola (the hyperbola in the diagram represents a cut parallel to the axis of the cone). View from above of, from left to right, a circle, an ellipse, a parabola and a hyperbola. When a plane intersects a cone at an angle that is parallel to the edge of the cone? A parabola is formed when a plane intersects a cone and that plane lies parallel to the edge of that cone. What conic section is formed when a cone is cut by a plane parallel to the vertical axis? hyperbola When a right circular cone is cut by a plane parallel to the axis the section view will be obtained?Explanation: If a cone made to cut by a plane parallel to its axis and some distance away from it the section formed is hyperbola. If the section plane is perpendicular to axis the section is circle. If section plane passes through apex the section formed is a triangle. When a cone is cut by planes at different angles the curves of intersection are called?Answer: In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane. When a cone is cut by a plane perpendicular? Explanation: If a cone made to cut by a plane parallel to its axis and some distance away from it the section formed is hyperbola. If the section plane is perpendicular to axis the section is circle. If section plane passes through apex the section formed is triangle. When we are cutting the cone parallel to its and generator then which of the following curve will be generated at the cutting surface? Explanation: When the plane cuts the cone parallel to the generator the curve traced out is Parabola. What happens when a plane intersects a cone?If you intersect a cone with a plane so that the plane is parallel to the base, you get a circle. A circle is defined as the set of all points whose distance from a fixed point (the center) is always the same. When the plane intersects the cone exactly at its vertex?Point: If the plane intersects the two cones at the vertex and at an angle greater than the vertex angle, we get a point. This is a degenerate ellipse. Line: If the plane intersects the two cones at the vertex and at an angle equal to the vertex angle, we get a line. This is a degenerate parabola. What can be formed when the plane is cutting parallel to the base? A circle is the conic section formed when the cutting plane is parallel to the base of the cone or equivalently perpendicular to the axis. When a right circular cone is cut by a plane? A right circular cone is cut by a plane parallel to its base in such a way that the slant heights of the original and the smaller cone thus obtained are in the ratio 2:1. What is the curve formed when a plane cuts a cone?When the plane cuts the cone at an angle between a perpendicular to the axis (which would produce a circle) and an angle parallel to the side of the cone (which would produce a parabola), the curve formed is an ellipse. What happens when you cut a cone at different angles?Angled view of a cone, with conic sections produced by cutting the cone at different angles. Cutting at right angles to the axis produces a circle. Cutting at less than a right angle to the axis but more than the angle made by the side of the cone produces an ellipse. What is the name of the conics formed if the plane? If the plane cuts at an angle to the axis but does not cut all the generators then what is the name of the conics formed? Explanation: If the plane cuts at an angle with respect to the axis and does not cut all the generators then the conics formed is a parabola. What is the conic section of a cone called? Explanation: When the plane cuts the cone at an angle parallel to the axis of the cone, then the resulting conic section is called as a hyperbola. If the plane cuts the cone at an angle with respect to the axis of the cone then the resulting conic sections are called as ellipse and parabola. |
A is produced when you slice a cone with a plane that is parallel to the base of the cone
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