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Given a right circular cone a plane that intersects the cone not at the vertex and is parallel to its edge will always result in a parabola regardless of the shape of the cone?
True
What is the definition of parabola?
There are several ways of defining a parabola. Here are some:Given a straight line and a point not on that line, a parabola is the locus of all points that are equidistant from that point (the focus) and the line (directrix).A parabola is the intersection of the surface of a right circular cone and a plane parallel to a generating line of that surface.A parabola is the graph of a quadratic equation.
What is a cone in 2D?
It depends on your the inclinantion of the plane which is used to "slice" the cone. The answer can be a circle, ellipse, parabola, hyperbola or two intersecting lines. These (apart from the last) are known as conic sections. In terms of the 2-d figure that generates a cone, the answer is a straight line, with a non-zero slope, rotated about the x-axis.
Parabola is the point at which the parabola is at its lowest or highest point?
A parabola is NOT a point, it is the whole curve.
What figure is formed by the intersection of a cone?
The most interesting intersections of cone are its planar sections (intersections with a plane). These sections are called "conic" The figures can be 1) dot - for plane going through apex 2) two lines - for plane containing cone axis 3) one line - for plane going through apex and touching the cone 3) circle - for plane orthogonal to cone axis 4) ellipsis - for plane that intersects the cone axis and generating lines 5) parabola - for plane parallel to a generating line 4) hyperbola - other cases See wikipedia's "conic section" article
What is the intersection of a cone and a plane parallel to a line along the side of a cone?
a parabola
Is there another not as common name for a parabola?
The parabola is a type of conic section, . The problem is that this is not a descriptive as the if the word "parabola" is used. The reason is that it is not the only geometric shape that can be derived by slicing a cone with a plane. Use the link below to see a drawing and learn more.
If a right circular cone intersects a plane that runs parallel to the edge of the cone what will be the result?
The intersection of the cone and that particular plane is a parabola.
If a right circular cone intersects a plane that runs parallel to the edge of the cone the resulting curve will be an?
A Parabola.
If a right circular cone intersects a plane that runs parallel to the edge of the cone the resulting curve will be?
Parabola
If a right circular cone intersects a plane that runs parallel to the edge of the cone the resulting curve is?
The "conic section" that is produced when a right circular cone intersects a plane that runs parallel to the edge of the cone is a parabola. In the case where the plane also intersects the vertex of the cone, the parabola becomes two intersecting lines.
What is the tilted away cross section of a cone?
Depends on the way you cut the cone, but the outline is either an ellipse or a parabola.
What is the geometric definition of parabola?
It is a section of a right circular cone by a plane that is parallel to one generating line of the cone.
Given a right circular cone a plane that intersects the cone not at the vertex and is parallel to its edge will always result in a parabola regardless of the shape of the cone?
True
Is a parabola formed when a plane slices through a double cone perpendicular to the bases of the cone?
No. A hyperbola is formed when a plane slices a cone perpendicular to the bases.
Which conic section is created if a plane that is parallel to the edge of a right circular cone intersects one nappe of the cone?
A parabola.
Is it true that given a right circular cone a plane that intersects the cone not at the vertex and is parallel to its edge will always result in a parabola regardless of the shape of the cone?
True.
