Transcript m14 konics - lokus

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.
Lokus
Jarak tegak
Garis lurus
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 nondegenerate 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
0
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
– 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