1. KONIK
LOKUS & CONIC SECTIONS

2. DEFINISI LOKUS
Lokus dalam dua matra merupakan lintasan suatu titik yang bergerak dalam satu satah dan mengikut syarat yang tertentu.
The path traced out by a point which moves under a certain condition is called the locus of the point.

3. LOKUS GARIS SELARI
Lokus bagi satu titik yang bergerak dengan jarak tegak yang sama dari suatu garis lurus,iaitu dua garis lurus yang selari dengan garis lurus tersebut dan jaraknya dari garis lurus tersebut adalah sama.
Garis lurus
Lokus
Jarak tegak

4. LOKUS BULATAN
Lokus bagi suatu titik yang bergerak dengan jarak yang sama dari satu titik tetap,iaitu satu bulatan yang berpusatkan titik tersebut.

5. CONIC SECTIONS
Conic sections can be viewed as non-degenerate curves generated by the intersections of a plane with one or two cones in a double cone.
These include
a pair of intersecting lines
a circle
a parabola
an ellipse
a hyperbola

6. CONIC SECTIONS
The four conic sections are the circle, the ellipse, the parabola, and the hyperbola
They are called conic sections because they are the shapes formed by the intersection of a plane with a conical surface.

7. CONIC SECTIONS
The type of conic section produced by this intersection depends on the angle at which the plane intersects the cone's surface.

8. THE CIRCLE
When a plane perpendicular to the axis of the cone intersects one of the cones, a circle is produced.

9. PARABOLA OR ELLIPSE
If the plane is not perpendicular to the axis and intersects only one cone, the curve produced is either an ellipse or a parabola.
Can you figure this out for yourself?

10. PARABOLA OR ELLIPSE

11. THE HYPERBOLA
The curve produced by a plane intersecting both the cones is a hyperbola.

12. MATHEMATICAL DEFINITION
Given a fixed point F (the focus), a fixed line d (the directrix), and a constant e (the eccentricity):
any conic can be defined as the locus of points P such that the ratio of the distance PF to the distance from P to the line d is equal to the eccentricity, e.

13. MATHEMATICAL DEFINITION
A conic section is defined as the locus of a point that moves such that the ratio of its distance from a fixed point (known as focus) in the plane to that from a fixed line (known as directrix) also in the plane, is a constant (known as its eccentricity).

15. LET’S EXPLORE CONICS!
This relationship can be seen in the following illustration

16. LET’S EXPLORE CONICS!
From your explorations, state the relationship between the conic sections and the value of e e
Conic section
circle
<1
ellipse 1
parabola
>1
hyperbola

17. THE PARABOLA
A parabola is the set of all points that are the same distance from a fixed line (called the directrix) and a fixed point (focus) not on the directrix.

18. Tutorial Aktiviti 1 Aktiviti 2 The Thought Experiment
Buat aktiviti ini secara berpasangan
Simpan (save) fail anda bagi setiap percubaan
Cetak fail tersebut dan masukkan cetakan itu dalam portfolio anda
Aktiviti 2
Buat aktiviti ini secara individu
Buat latihan untuk melakarkan lokus dengan menggunakan perisian GSP (Rujuk edaran Using the Locus Menu in GSP)
Cetak hasil kerja anda dan masukkan dalam portfolio anda