KONIK LOKUS & CONIC SECTIONS

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.

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

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

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

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.

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

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

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?

PARABOLA OR ELLIPSE

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

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.

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).

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

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

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.

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