What conic section can be formed if the cutting plane is parallel to one and only one generator?
In figure a below, we have a cone and a cutting plane which is parallel to one and only one generator of the cone. This conic is a parabola.
What are the 4 conic sections?
A conic is the intersection of a plane and a right circular cone. The four basic types of conics are parabolas, ellipses, circles, and hyperbolas. Study the figures below to see how a conic is geometrically defined. In a non-degenerate conic the plane does not pass through the vertex of the cone.
What conic is formed when the cutting plane is parallel to the generator?
When a cutting plane which is parallel to one and only one generator of the cone the conic is a parabola. If the cutting plane is parallel to two generators, this intersects nappes of the cone, and a hyperbola is obtained.
What happens to the ellipse when the cutting plane becomes parallel with the bases?
Conic sections – Ellipse (the others are an circle, parabola and hyperbola). In the above figure, there is a plane* that cuts through a cone. When the plane is parallel to the cone’s base, the intersection of the cone and plane is a circle. But if the plane is tilted, the intersection becomes an ellipse.
What conic section is formed if the plane is parallel to the base of the cone?
circle
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.
What is formed when a plane cuts through a generator?
Explanation: If the plane cuts all the generators and is at an angle to the axis of the cone, then the resulting conic section is called as an ellipse. If the cutting angle was right angle and the plane cuts all the generators then the conic formed would be circle.
What are the 5 conic sections?
Depending on the angle between the plane and the cone, four different intersection shapes can be formed. The types of conic sections are circles, ellipses, hyperbolas, and parabolas. Each conic section also has a degenerate form; these take the form of points and lines.
What are the 3 degenerate conics?
There are three types of degenerate conics: a single point, a line or two parallel lines, or two intersecting lines.
What can be formed when the plane is cutting parallel to the base?
Circle. A circle is formed when the plane is parallel to the base of the cone. Its intersection with the cone is therefore a set of points equidistant from a common point (the central axis of the cone), which meets the definition of a circle.
What is the conic section formed when a cone is cut by a plane parallel to its base and not passing through the vertex?
Conic sections are obtained by passing a cutting plane to a right circular cone. For a cutting plane parallel to the axis of the cone not passing through the vertex, the section formed is hyperbola .
When the cutting plane is parallel to the axis of the cone The section is a?
hyperbola
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 the cutting plane is parallel to an element the resulting curve is called a?
Parabola. A parabola is formed when the plane is parallel to the surface of the cone, resulting in a U-shaped curve that lies on the plane.
What is the difference between cutting plane line and revolved section?
A cutting plane line does not need to be shown, since the location of the cut is obvious. A revolved section shows the shape of an object by rotating a section 90 degrees to face the viewer. The three revolved sections illustrated in the spear-like object of figure 12 show the changes that take place in its shape.
What is the difference between cutting plane and half section?
As in all sectional drawings, the cutting plane take precedence over the center line. Here is another example of a half section. Remember that only one fourth of the object is removed with a half section, whereas half of the object is generally removed with a full section.
How can an object be sectioned in a sectional view?
Just as an apple can be sectioned any way you choose, so can an object in a sectional view of a drawing or sketch. A surface cut by the saw in the drawing above is a cutting plane. Actually, it is an imaginary cutting plane taken through the object, since the object is imagined as being cut through at a desired location.
What is the difference between parallel cross section and perpendicular cross-section?
In parallel cross-section, a plane cuts the solid shape in the horizontal direction (i.e., parallel to the base) such that it creates the parallel cross-section In perpendicular cross-section, a plane cuts the solid shape in the vertical direction (i.e., perpendicular to the base) such that it creates a perpendicular cross-section