# Conic Section

## Overview

### What plane shapes may you get if you cut a carrot (right circular cone) with a knife at different angles?

Let AB and CD be two fixed lines intersecting at the point O at an angle (0° < θ < 90°). If the plane containing these two lines AB and CD is rotated about the line CD, then the surface generated by AB is called the right circular cone. O is the vertex, the CD is the vertical axis, θ is the vertical angle and AB is the generator of the cone.

Take the solid cone and cut them with a sharp knife:

- Cut the cone parallel to the base. The section between cone and plane is said to be a circle.
- Cut the cone parallel to slant edge of the cone. The section in between cone and plane is said to be parabola.
- Cut the cone in such a way that the angle between plane and axis of cone is greater than vertical angle of cone. But less than 90°. the section in between cone and the plane is said to be ellipse.
- Intersect double circular cone parallel to edge of the cone (slant edge). The pair of parabola or the sections formed between double cone and plane is said to be hyperbola.

## Exercise

Name the different parts of the cone indicated by a, b, c, d and e.

b = upper nappe

d = generator

e = vertex

a = axis

c = lower nappe

d = generator

e = vertex

a = axis

c = lower nappe

Name the conic section from following figures.

a = ellipse

b = parabola

c = circle

d = hyperbola

b = parabola

c = circle

d = hyperbola