first lesson introduction first module 1

This is the first lessons semester 1

1. Precalculus
Science, Technology, Engineering, and Mathematics
Lesson 1
Introduction to Conic
Sections

2. 2
Illustrate the different types of conic sections:
parabola, ellipse, circle, hyperbola, and
degenerate cases (STEM_PC11AG-ia-1)
Learning Competency

3. 3
●Generate conic sections from the intersection of a
plane and a cone.
●Identify the conic sections: parabola, ellipse, circle,
hyperbola, and degenerate cases.
Objectives

4. 4

5. 5

6. 6
Conic
Sections

7. 7
Conic sections are obtained from the intersection
between a double-napped cone and a plane.

8. Parabolas are
formed when the
plane is parallel to
the generating
line of one cone.
PARABOLA
8

9. Ellipses are
formed when the
plane intersects
the one cone at
an angle other
than 90°.
ELLIPSE
9

10. Hyperbolas are
formed when the
plane is parallel to
the axis of
revolution or the
??????-axis.
HYPERBOLA
10

11. Circles are
formed when the
intersection of the
plane is
perpendicular to
the axis of
revolution.
CIRCLE
11

12. 12
Degenerate conic sections are formed when a plane
intersects the cone in such a way that it passes through
the apex.
Degenerate Conic Sections

13. 13
Degenerate Conic Sections
Point

14. 14
Degenerate Conic Sections
Point

15. 15
Degenerate Conic Sections
Line

16. 16
Degenerate Conic Sections
Line

17. 17
Degenerate Conic Sections
Two Intersecting Lines

18. 18
Degenerate Conic Sections
Two Intersecting Lines

19. 19
Degenerate Conic Sections

20. 20
Identify the conic section or the part that is being
described.
1. These are the conic sections that are formed when the
plane intersects the double-napped cone in a way that it
passes through the apex.
2. This conic section is formed when the plane is parallel to
the axis of revolution.
3. It is the midpoint of the two foci for ellipse and
hyperbola.

21. 21
Determine the type of
conic sections shown at
the right.