Mathematics Project…
conic section
Task 1
Introduction
 Circle:- is a simple shape of Euclidean geometry that is the set of all points in a
plane that are a given distance from a given point, the centre. The distance between
any of the points and the centre is called the radius. It can also be defined as the
locus of a point equidistant from a fixed point.
 Ellipse:- An ellipse, informally, is an oval or a "squished" circle. In "primitive" geometrical
terms, an ellipse is the figure you can draw in the sand by the following process: Push two sticks
into the sand. Take a piece of string and form a loop that is big enough to go around the two
sticks and still have some slack. Take a third stick, hook it inside the string loop, pull the loop taut
by pulling the stick away from the first two sticks, and drag that third stick through the sand at
the furthest distance the loop will allow. The resulting shape drawn in the sand is an ellipse.
Task 1
Introduction
 Parabola:- The line perpendicular to the directrix and passing through the focus (that is,
the line that splits the parabola through the middle) is called the "axis of symmetry". The point
on the axis of symmetry that intersects the parabola is called the "vertex", and it is the point
where the curvature is greatest. The distance between the vertex and the focus, measured along
the axis of symmetry, is the "focal length". Parabolas can open up, down, left, right, or in some
other arbitrary direction. Any parabola can be repositioned and rescaled to fit exactly on any
other parabola — that is, all parabolas are similar.
 Hyperbola:- hyperbolas don't come up much — at least not that I've noticed —
in other math classes, but if you're covering conics, you'll need to know their basics.
An hyperbola looks sort of like two mirrored parabolas, with the two "halves" being
called "branches". Like an ellipse, an hyperbola has two foci and two vertices; unlike
an ellipse, the foci in an hyperbola are further from the hyperbola's center than are.
Conic section uses..
 the paths of the planets around the sun are ellipses with the
sun at one focus
 Hyperbolas: are used in a navigation system known as
LORAN (long range navigation)
 Parabola: is used in the design of car headlights and in
spotlights because it aids in concentrating the light beam
 Circle :To find the wheels on a bicycle. wheels of a car, tire
Picture of conic section
Parabola
circle
Ellipse
Task 2
Comprehensive comparison between conics
Circle
Ellipse
Parabola
Hyperbola
Closed or open curve.
Closed
Closed
Opened
Opened
Definition
The set of all points in
a plane that are
equidistant from a
given point in the
plane called the center
The set of all points in
a plane such that the
sum of the distance
from two fixed points
is constant. These two
points are called the
foci of the ellipse
The set of all points in
a plane that are the
same distance from a
given points called the
focus and a given line
called the diretrix.
The set of all points in
a plane such that the
absolute value of the
differences of the
distance from the foci
is constant
Equation
X2+Y2=R2
X2/a+y2/b
y2 = 4ax
x2//a2-y2/b2
There is on focus
On the vertices
The same side of the
opening
The same side of the
opening
Radius
Diameter
Major
Minor
DirectX
Focus
Vertex
DirectX
Focus
Vertex
Relation between its
center and focus (foci)
Other properties
Task 2
Comprehensive comparison between conics
 Graph …
Circle
Ellipse
Parabola
Hyperbola
Task 3
 1-Parabola:
Task 3
 2-Circle:
Task 4
 1-Physics:
Task 4
 2-Halley’s Comet
Focus ( h , k + 1/4a )
1 = -80a
K+1/4a = 0
a = -1/80
20+1/4a = 0
y = a (x-h)2 + k
1/4a = -20
y = -1/80(x-0)2+20
y = -1/80 x2 +20
Thanks for watching
 Done by:
1-Saif Abdulla
2-Rashid Salem
3-Rashid Saeed
 Class:
12-01