 # How can we obtain a line when a plane cut the cone? Explain with the help of 3-D diagram. 4 years ago
Dear student

## Sections of a Cone

It depends upon the location of the plane with reference to the cone and the angle made by the vertical axis and the intersecting plane, that what kind of conic section we get.

Let the angle between intersecting plane and the vertical axis be ∅.

If the plane cuts the one nappe of the cone, such that,

• Ɵ ellipse.

• ∅ = 90°, when the plane is perpendicular at the axis, or the angle of intersection of plane and the vertical axis is equal to 90°, the ellipse becomes the circle. Or you can say that circle is the special type of ellipse, the section is circle.

• Ɵ = ∅, when the angle between the vertical axis and the plane is equal to the vertex angle, we get an open curve called Parabola at the intersecting surface of the cone.

• If the plane cuts the two nappes of the cone, such that,

• Ɵ Hyperbola.

## Degenerate conics

If a plane intersects the double right circular cone at the vertex of the cone, such that

• When Ɵ point .

• When Ɵ = ∅, in case of parabola, the plane contains a generator of the cone and the section is a straight line.

• When 0 ≤ Ɵ pair of intersecting straight lines 