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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?
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If a right circular cone intersects a plane that runs parallel to the cone's axis but does not pass through its vertex the resulting curve will be an?
hyperbola
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.
Where is the axis of symmetry of a parabola located?
Parallel to the y-axis, going through the highest/lowest point of the parabola (if the parabola is negative/positive, respectively).
Does a transversal line have to intersect with two parallel lines?
Yes, a transversal line always intersects two parallel lines.
Is it true that if a transversal intersects two parallel lines then corresponding angles are supplementary?
yes !
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.
Is it true that if 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?
Yes, it is true that if 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. There are four cases... Plane perpendicular to axis: circlePlane between perpendicular to axis and parallel to edge: ellipsePlane parallel to edge: parabolaPlane between parallel to edge and parallel to axis: hyperbolehttp://en.wikipedia.org/wiki/Conic_section
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.
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 will be an?
A Parabola.
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.
If a right circular cone intersects a plane that runs parallel to the cones axis but does not pass through its vertex the resulting curve will be a?
parabola
If a Right circular cone intersects a plane that runs parallel to the cone's axis but does not pass through its vertex the resulting curve will be what?
parabola
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 result curve will be?
If a right circular cone intersects a plane that runs parallel to the edge of the cone the result curve will be a parabola, unless the intersection includes the vertex of the cone, in which case the intersection is a straight line. This is a conic section. Depending on the angle of the plane, the section will be a circle, an ellipse, a parabola, or two hyperboles.
If a right circular cone intersects a plane that runs parallel to the edge of the cone is what?
The intersection of a right circular cone and a plane that is parallel to the edge of the cone is a parabola. However, if the vertex of the cone lies on the plane, then the intersection is simply two intersecting lines.
If a right circular cone intersects a plane that runs parallel to the cone's axis but does not pass through its vertex?
If a right circular cone intersects a plane that runs parallel to the cone's axis but does not pass through its vertex, the resulting curve is a pair of hyperboles.
