The document provides an overview of conic sections, including types such as parabolas, ellipses, circles, hyperbolas, and degenerate cases. It defines conic sections as the intersection of a plane and a right circular cone. Additionally, it illustrates how different orientations of the plane lead to the various types of conic sections.

1. Introduction to
Conic Sections
Prepared by: Teacher CARL

2. Learning Outcomes
At the end of the lesson, the student is able to:
• (1) illustrate the different types of conic sections: parabola,
ellipse, circle, hyperbola, and degenerate cases

3. CONIC SECTION
•A conic section is the
intersection of a
plane and a right
circular cone with two
nappes.

4. CONIC SECTION
• A degenerate conic is either a point, a circle, or two
intersecting lines.

5. CONIC SECTION
• Circle (Figure 1.1) - when the
plane is horizontal
• Ellipse (Figure 1.1) - when
the (tilted) plane intersects
only one cone to form a
bounded curve.
Figure 1.1

6. CONIC SECTION
• Parabola (Figure 1.2) - when
the plane intersects only one
cone to form an unbounded
curve
Figure 1.2

7. CONIC SECTION
• Hyperbola (Figure 1.3) - when
the plane (not necessarily
vertical) intersects both cones
to form two unbounded
curves (each called a branch
of the hyperbola)
Figure 1.3

8. THANK YOU