Question

Which of the following conic sections could be formed when a plane intersects a cone at a shallow, non-zero angle to the base without intersecting the base itself?

a. Circle
b. Parabola
c. Ellipse
d. Hyperbola

Answer 1

A plane intersecting a cone at a shallow, non-zero angle to the base without intersecting the base itself can form an ellipse or a hyperbola.

Step-by-step explanation:

When a plane intersects a cone at a shallow, non-zero angle to the base without intersecting the base itself, it can form either an ellipse or a hyperbola.

An ellipse is a closed curve that looks like a stretched circle, while a hyperbola is a curve that opens up and down or left and right.

A circle (option a) is formed when the plane intersects the cone at a right angle to the base, and a parabola (option b) is formed when the plane intersects the cone parallel to the base.