Question

question 10 of 25
if a right circular cone is intersected by a plane that is parallel to one edge of the cone, as in the picture below, what shape is produced?
a. a parabola
b. a hyperbola
c. a circle
d. an ellipse
e. a line
f. a point

Explanation:

When a right - circular cone is intersected by a plane parallel to one edge of the cone, the resulting conic section is a parabola. This is a fundamental property of conic sections. A circle is formed when the plane is perpendicular to the axis of the cone. An ellipse is formed when the plane is at an angle (not parallel to an edge and not perpendicular to the axis). A hyperbola is formed when the plane intersects both nappes of the cone. A line and a point are degenerate cases (for example, a plane tangent to the cone gives a line in a degenerate case, and a plane passing through the vertex and not intersecting the cone otherwise gives a point in a degenerate case). Since the plane is parallel to one edge of the cone, by the definition and properties of conic - section formation, the shape is a parabola.

Answer:

A. A parabola