Question

A cone is cut by a plane as shown, where the plane is not parallel to the base. The cross-section of the cone and the plane is

A) a circle.
B) an ellipse.
C) a parabola.
D) a hyperbola.

Answer 1

Option (b) is correct.

The cross-section of the cone and the plane is an ellipse.

Explanation:

Given : A cone is cut by a plane as shown, where the plane is not parallel to the base.

We have to determine the shape of the cross-section of the cone and the plane.

Since, The cone is cut by the plane which is not parallel to its base.

a > b

There a is the horizontal distance between the slant height of cone.

and b is vertical distance.

Thus, when a > b

`(x^2)/(a^2)+(y^2)/(b^2) =1`

Thus, The cross-section of the cone and the plane is an ellipse.