If a right circular cone intersects a plane that runs parallel to the edge of the cone, the resulting curve will be a(n) _____.A.hyperbolaB.ellipseC.parabolaD.circle
Question
If a right circular cone intersects a plane that runs parallel to the edge of the cone, the resulting curve will be a(n) _____.A.hyperbolaB.ellipseC.parabolaD.circle
Solution
The answer is C. Parabola.
Here's why:
A right circular cone is a three-dimensional geometric shape that tapers smoothly from a flat, round base to a point called the apex or vertex. If a plane intersects a cone and runs parallel to the edge (or side) of the cone, the resulting curve will be a parabola.
This is because a parabola is defined as the set of all points in the plane that are equidistant from a given line (the directrix) and a given point (the focus) not on the line. In this case, the directrix is the base of the cone and the focus is the apex of the cone. The plane that intersects the cone and runs parallel to its edge cuts through the cone in such a way that it satisfies this definition, resulting in a parabolic curve.
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