Question

Which of the following conic sections could be formed when a plane intersects both cones of a double cone?

1) Circle
2) Ellipse
3) Parabola
4) Hyperbola

Answer 1

Circle, Ellipse, Parabola, and Hyperbola can all be formed by a plane's intersection with a double cone, with the specific conic section depending on the angle and position of the cutting plane.

Step-by-step explanation:

The conic sections that could be formed when a plane intersects both cones of a double cone are a circle, ellipse, parabola, and hyperbola. These shapes are created depending on the angle and position of the plane in relation to the cones. A circle is formed when the plane intersects the cone at a right angle to its axis. An ellipse is similar but with the plane at an angle that is not perpendicular. A parabola is created when the plane is parallel to a slant of the cone. Finally, a hyperbola results when the plane intersects both halves of the double cone.